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RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A

July 18, 2018 by Veerendra

RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A

These Solutions are part of RS Aggarwal Solutions Class 10. Here we have given RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A

Other Exercises

  • RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A
  • RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10B
  • RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10C
  • RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10D

Exercise 10A

RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A a1

RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A a2

Question 1:

(i)   x2-x+3=0 is a quadratic polynomial.
∴  x2-x+3=0 is a quadratic equation.

(ii) 2x2+ \(\frac { 5 }{ 2 }   \)x-√3=0
⇒ 4x2+5x-2√3=0
Clearly is 4x2+5x-2√3=0 a quadratic polynomial.
∴ 2x2+ \(\frac { 5 }{ 2 }   \)x-√3=0 is a quadratic equation.

(iii) √2x2+7x+5√2=0 is a quadratic polynomial.
∴ √2x2+7x+5√2=0 is a quadratic equation.

(iv)\(\frac { 1 }{ 3 }   \)x2+\(\frac { 1 }{ 5 }   \)x-2=0
⇒ 5x2+3x-2=0
Clearly, 5x2+3x-2=0 is a quadratic equation.
\(\frac { 1 }{ 3 }   \)x2+\(\frac { 1 }{ 5 }   \) is a quadratic equation.

(v) x2-3x-√x+4=0 is not a quadratic polynomial since it contains √x, in which power 1/2 of x is not an integer.
∴ x2-3x-√x+4=0 is not a quadratic equation.

(vi) x-\(\frac { 6}{ x }   \)=3
⇒ x2-3x-6 =0
And (x2-3x-6)Being a polynomial of degree 2, it is a quadratic polynomial.
Hence, x-\(\frac { 6}{ x }   \)=3 is a quadratic equation.

(vii) x+\(\frac { 2}{ x }   \)= x2
⇒ x3-x2-2 =0
And (x3-x2-2 =0) being a polynomial of degree 3, it is not a quadratic polynomial.
Hence, x+\(\frac { 2}{ x }   \)= x2 is not a quadratic equation.

(viii) \({ x }^{ 2 }-\frac { 1 }{ { x }^{ 2 } } =5  \) ⇒ x4 -1=5x2
⇒x4-5x2-1 =0
And (x4-5x2-1 =0) being a polynomial of degree 4.
Hence \({ x }^{ 2 }-\frac { 1 }{ { x }^{ 2 } } =5  \) is not a quadratic equation.

Solving A Quadratic Equation By Completing The Square

Question 2:
The given equation is 3x2+2x-1=0
(i) On substituting x = -1 in the equation, we get
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 2.1
(ii) On substituting \(x=\frac { 1 }{ 3 }   \) in the equation, we get
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 2.2
(iii) On substituting \(x=-\frac { 1 }{ 2 }    \) in the equation , we get
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 2.3

More Resources

  • RS Aggarwal Solutions Class 10
  • RD Sharma Class 10 Solutions
  • NCERT Solutions

Question 3:
Since x = 1 is a solution of x2+kx+3=0 it must satisfy the equation.
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 3.1
Hence the required value of k = -4
Question 4:
Since \(x=\frac { 3 }{ 4 }   \) is a root of  ax2+bx-6=0, we have
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 4.1
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 4.2
Again x = -2 being a root of ax2+bx-6=0, we have
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 4.3
Multiplying (2) by 4 adding the result from (1), we get
11a = 44 ⇒ a = 4
Putting a = 4 in (1), we get
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 4.4
Question 5:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 5.1
Question 6:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 6.1
Question 7:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 7.1
Hence, 9 and -9 are the roots of the equation 3x2-243=0.
Question 8:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 8.1
Hence, -5 and -7 are the roots of x2+12x+35=0.
Question 9:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 9.1
Hence, 11 and 7 are the roots of equation x2=18x-77
Question 10:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 10.1
Hence, \(x=-\frac { 1 }{ 3 }    \) is the repeated root of the equation 9x2+6x+1=0
Question 11:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 11.1
Hence,  is the repeated root of the equation
Question 12:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 12.1
Hence, \(x=-\frac { 3 }{ 2 }   \), \(x=-\frac { 1 }{ 2 }   \)are the roots of 6x2+11x+3=0
Question 13:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 13.1
Hence, \(x=\frac { 4 }{ 3 }   \) and \(x=-\frac { 3 }{ 2 }   \) are the roots of equation 6x2+x-12=0

Question 14:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 14.1
Hence, \(x=-\frac { 1 }{ 3 }   \) and 1 are the roots of the equation 3x2-2x-1=0.
Question 15:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 15.1
Hence, \(x=\frac { 2 }{ 3 }   \) and \(x=-\frac { 1 }{ 2 }   \)are the roots of equation 6x2-x-2=0.
Question 16:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 16.1
Hence, \(x=-\frac { 1 }{ 16 }   \) and \(x=\frac { 2 }{ 3 }   \) are the roots of 48x2-13x-1=0.
Question 17:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 17.1
Hence, \(x=-\frac { 5 }{ 3 }   \) and x=-2 are the roots of the equation 3x2+11x+10=0
Question 18:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 18.1
Hence,\(x=\frac { 25 }{ 4 }   \) and x=-4 are the roots of the equation 4x2-9x=100.
Question 19:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 19.1
Hence,  \(x=\frac { 4 }{ 9 }   \) and 2 are the roots of the equation 9x2-22+8=0
Question 20:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 20.1
Hence,  \(x=\frac { 7 }{ 5 }   \) and \(x=-\frac { 4 }{ 3 }   \) are the roots of the given equation 15x2-28=x.
Question 21:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 21.1
Hence, \(x=\frac { 1 }{ 3 }   \) and -4 are the roots of given equation .
Question 22:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 22.1
Hence, 1 and  √2 are the roots of the given equation
Question 23:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 23.1
Question 24:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 24.1
Question 25:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 25.1
Hence, \(\frac { -\sqrt { 7 }  }{ 3 }      \) and \(\frac { \sqrt { 7 }  }{ 7 }     \) are the roots of given equation.
Question 26:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 26.1
Hence, -√7 and \(\frac { 13\sqrt { 7 }  }{ 7 }     \) are the roots of given equation.
Question 27:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 27.1
Hence, \(\frac { 2\sqrt { 6 }  }{ 3 }     \) and  \(\frac { -\sqrt { 6 }  }{ 8 }     \)are the roots of given equation.
Question 28:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 28.1
Hence, 5 and \(-\frac { 7 }{ 5 }    \)are the roots of given equation
Question 29:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 29.1
Hence, \(-\frac { 1 }{ 5 }    \) and \(\frac { 1 }{ 2 }    \)are the roots of given equation.
Question 30:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 30.1
Hence, 2 and  \(\frac { 1 }{ 2 }    \) are the roots of given equation.
Question 31:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 31.1
Hence, \(-\frac { b }{ a }    \) and \(\frac { c }{ b }    \) are the roots of given equation.
Question 32:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 32.1
Hence, \(\frac { -1 }{ { a }^{ 2 } }     \) and \(\frac { 1 }{ { b }^{ 2 } }     \)are the roots of given equation.
Question 33:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 33.1
Hence, \(\frac { 3a }{ 4b }    \) and \(\frac { -2b }{ 3a }    \) are the roots of given equation.
Question 34:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 34.1
Hence, \(\frac { { a }^{ 2 } }{ 2 }      \) and \(\frac { { b }^{ 2 } }{ 2 }      \)are the roots of given equation.
Question 35:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 35.1
Hence, 2 and 1 are the roots of the given equation
Question 36:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 36.1
Hence, -9 and 7 are the roots of the given equation
Question 37:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 37.1
Hence, -4 and \(\frac { 9 }{ 4 }    \) are the roots of the given equation
Question 38:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 38.1
Hence  \(\frac { 40 }{ 13 }    \) and 6 are the roots of the given equation
Question 39:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 39.1
Hence, 4 and \(-\frac { 2 }{ 9 }    \) are the roots of the given equation
Question 40:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 40.1
Hence, 3 and \(\frac { 4 }{ 3 }    \) are the roots of the given equation.
Question 41:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 41.1
Hence, 5 and \(\frac { 1 }{ 2 }    \) are the roots of the given equation.
Question 42:
Putting RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 42.1 the given equation become
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 42.2
Case I:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 42.3
Case II:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 42.4
Hence, \(-\frac { 3 }{ 2 }    \) and -2 are the roots of the given equation
Question 43:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 43.1
Putting RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 43.2 the given equation become
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 43.3
Case I:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 43.4
Case II:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 43.5
Hence, -1 and \(-\frac { 23 }{ 5 }    \) are the roots of the given equation
Question 44:
On putting RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 44.1 the given equation become
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 44.2
Case I:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 44.3
Case II:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 44.4
Hence, -10 and \(-\frac { 1 }{ 5 }    \) are the roots of the given equation.
Question 45:
Putting RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 45.1 the given equation become
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 45.2
Case I:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 45.3
Case II:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 45.4
Hence, -1 and \(\frac { 1 }{ 8 }    \) are the roots of the given equation
Question 46:
The given equation
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 46.1
Hence, (a+b) and \(\frac { (a+b) }{ 2 }  \) is the roots of the given equation
Question 47:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 47.1
Hence, \(\frac { a+b }{ ab }   \) and \(\frac { 2 }{ a+b }   \) are the roots of the given equation
Question 48:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 48.1
Hence, -2,0 are the roots of the given equation
Question 49:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 49.1
Hence,  \(\frac { 1 }{ 2 }    \) and \(\frac { 1 }{ 2 }    \) are the roots of the given equation
Question 50:
RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A 50.1
Hence, 3 and 2 are the roots of the given equation.

Hope given RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A are helpful to complete your math homework.

If you have any doubts, please comment below. A Plus Topper try to provide online math tutoring for you.

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