Nature Of The Roots Of A Quadratic Equation The nature of the roots depends on the value of b2 – 4ac. bx2 – 4ac is called the discriminant of the quadratic equation ax2 + bx + c = 0 and is generally, denoted by D. ∴ D = b2 – 4ac If D > 0, i..e., b2 – 4ac > 0, i.e., b2 – 4ac is positive; the roots are real and unequal. Also, (i) If b2 – 4ac is a perfect square, the … [Read more...] about Nature Of The Roots Of A Quadratic Equation
Mathematics
How Do You Determine The Degree Of A Polynomial
Degree Of A Polynomial The greatest power (exponent) of the terms of a polynomial is called degree of the polynomial. For example : In polynomial 5x2 – 8x7 + 3x: (i) The power of term 5x2 = 2 (ii) The power of term –8x7 = 7 (iii) The power of 3x = 1 Since, the greatest power is 7, therefore degree of the polynomial 5x2 – 8x7 + 3x is 7 The degree of polynomial : (i) 4y3 … [Read more...] about How Do You Determine The Degree Of A Polynomial
Algebraic Methods Of Solving A Pair Of Linear Equations
Algebraic Methods Of Solving A Pair Of Linear Equations Sometimes, graphical method does not give an accurate answer. While reading the coordinates of a point on a graph paper, we are likely to make an error. So, we require some precise method to obtain accurate result. Algebraic methods given below yield accurate answers. (i) Method of elimination by substitution (ii) … [Read more...] about Algebraic Methods Of Solving A Pair Of Linear Equations
Geometric Meaning Of The Zeroes Of A Polynomial
Geometric Meaning Of The Zeroes Of A Polynomial Let us consider linear polynomial ax + b. The graph of y = ax + b is a straight line. For example : The graph of y = 3x + 4 is a straight line passing through (0, 4) and (2, 10). (i) Let us consider the graph of y = 2x – 4 intersects the x-axis at x = 2. The zero 2x – 4 is 2. Thus, the zero of the polynomial 2x – 4 is … [Read more...] about Geometric Meaning Of The Zeroes Of A Polynomial
Types Of Polynomials
Types Of Polynomials (i) Based on degree : If degree of polynomial is Examples 1. One Linear x + 3, y – x + 2, √3x –3 2. Two Quadratic 2x2 –7, , x2 +1+ 3y 3. Three Cubic x3 + 3x2 –7x+8, 2x2+5x3+7, 4. Four bi-quadratic x4 + y4 + 2x2y2, x4 + 3,… (ii) Based on Terms : If number of terms in polynomial … [Read more...] about Types Of Polynomials