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**RS Aggarwal Class 10 Solutions Chapter 10 Quadratic Equations**

**Exercise 10A**

**Question 1:**

(i) x^{2}-x+3=0 is a quadratic polynomial.

∴ x^{2}-x+3=0 is a quadratic equation.

(ii) 2x^{2}+ x-√3=0

⇒ 4x^{2}+5x-2√3=0

Clearly is 4x^{2}+5x-2√3=0 a quadratic polynomial.

∴ 2x^{2}+ x-√3=0 is a quadratic equation.

(iii) √2x^{2}+7x+5√2=0 is a quadratic polynomial.

∴ √2x^{2}+7x+5√2=0 is a quadratic equation.

(iv)x^{2}+x-2=0

⇒ 5x^{2}+3x-2=0

Clearly, 5x^{2}+3x-2=0 is a quadratic equation.

x^{2}+ is a quadratic equation.

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

∴ x^{2}-3x-√x+4=0 is not a quadratic equation.

(vi) x-=3

⇒ x^{2}-3x-6 =0

And (x^{2}-3x-6)Being a polynomial of degree 2, it is a quadratic polynomial.

Hence, x-=3 is a quadratic equation.

(vii) x+= x^{2}

⇒ x^{3}-x^{2}-2 =0

And (x^{3}-x^{2}-2 =0) being a polynomial of degree 3, it is not a quadratic polynomial.

Hence, x+= x^{2} is not a quadratic equation.

(viii) ⇒ x^{4} -1=5x^{2}

⇒x^{4}-5x^{2}-1 =0

And (x^{4}-5x^{2}-1 =0) being a polynomial of degree 4.

Hence is not a quadratic equation.

Solving A Quadratic Equation By Completing The Square

**Question 2:**

The given equation is 3x^{2}+2x-1=0

(i) On substituting x = -1 in the equation, we get

(ii) On substituting in the equation, we get

(iii) On substituting in the equation , we get

**Question 3:**

Since x = 1 is a solution of x^{2}+kx+3=0 it must satisfy the equation.

Hence the required value of k = -4

**Question 4:**

Since is a root of ax^{2}+bx-6=0, we have

Again x = -2 being a root of ax^{2}+bx-6=0, we have

Multiplying (2) by 4 adding the result from (1), we get

11a = 44 ⇒ a = 4

Putting a = 4 in (1), we get

**Question 5:**

**Question 6:**

**Question 7:**

Hence, 9 and -9 are the roots of the equation 3x^{2}-243=0.

**Question 8:**

Hence, -5 and -7 are the roots of x^{2}+12x+35=0.

**Question 9:**

Hence, 11 and 7 are the roots of equation x^{2}=18x-77

**Question 10:**

Hence, is the repeated root of the equation 9x^{2}+6x+1=0

**Question 11:**

Hence, is the repeated root of the equation

**Question 12:**

Hence, , are the roots of 6x^{2}+11x+3=0

**Question 13:**

Hence, and are the roots of equation 6x^{2}+x-12=0

**Question 14:**

Hence, and 1 are the roots of the equation 3x^{2}-2x-1=0.

**Question 15:**

Hence, and are the roots of equation 6x^{2}-x-2=0.

**Question 16:**

Hence, and are the roots of 48x^{2}-13x-1=0.

**Question 17:**

Hence, and x=-2 are the roots of the equation 3x^{2}+11x+10=0

**Question 18:**

Hence, and x=-4 are the roots of the equation 4x^{2}-9x=100.

**Question 19:**

Hence, and 2 are the roots of the equation 9x^{2}-22+8=0

**Question 20:**

Hence, and are the roots of the given equation 15x^{2}-28=x.

**Question 21:**

Hence, and -4 are the roots of given equation .

**Question 22:**

Hence, 1 and √2 are the roots of the given equation

**Question 23:**

**Question 24:**

**Question 25:**

Hence, and are the roots of given equation.

**Question 26:**

Hence, -√7 and are the roots of given equation.

**Question 27:**

Hence, and are the roots of given equation.

**Question 28:**

Hence, 5 and are the roots of given equation

**Question 29:**

Hence, and are the roots of given equation.

**Question 30:**

Hence, 2 and are the roots of given equation.

**Question 31:**

Hence, and are the roots of given equation.

**Question 32:**

Hence, and are the roots of given equation.

**Question 33:**

Hence, and are the roots of given equation.

**Question 34:**

Hence, and are the roots of given equation.

**Question 35:**

Hence, 2 and 1 are the roots of the given equation

**Question 36:**

Hence, -9 and 7 are the roots of the given equation

**Question 37:**

Hence, -4 and are the roots of the given equation

**Question 38:**

Hence and 6 are the roots of the given equation

**Question 39:**

Hence, 4 and are the roots of the given equation

**Question 40:**

Hence, 3 and are the roots of the given equation.

**Question 41:**

Hence, 5 and are the roots of the given equation.

**Question 42:**

Putting the given equation become

Case I:

Case II:

Hence, and -2 are the roots of the given equation

**Question 43:**

Putting the given equation become

Case I:

Case II:

Hence, -1 and are the roots of the given equation

**Question 44:**

On putting the given equation become

Case I:

Case II:

Hence, -10 and are the roots of the given equation.

**Question 45:**

Putting the given equation become

Case I:

Case II:

Hence, -1 and are the roots of the given equation

**Question 46:**

The given equation

Hence, (a+b) and is the roots of the given equation

**Question 47:**

Hence, and are the roots of the given equation

**Question 48:**

Hence, -2,0 are the roots of the given equation

**Question 49:**

Hence, and are the roots of the given equation

**Question 50:**

Hence, 3 and 2 are the roots of the given equation.

Bro says

Please give Sol of new RS Agarwal edition

Surabhi Singh says

It’s give nice solution but it is of old edition

Please give solutions of new r.s. aggarwal edition