HOW TO FIND THE QUADRATIC EQUATION WITH THE SUM AND PRODUCT OF ROOTS

How to Find the Quadratic Equation with the Sum and Product of Roots :

Here we are going to see how to find quadratic equation when sum and product of roots are given.

General Form of Quadratic Equation with Sum and Product of Zeros

x^{2} - (sum of roots) x + product of roots = 0

(or)

x^{2} - (a + ᵦ)x + a ᵦ = 0

How to Find the Quadratic Equation with the Sum and Product of Roots - Questions

Question 1 :

Determine the quadratic equations, whose sum and product of roots are

(i) -9, 20

Solution :

x^{2} - (sum of roots) x + product of roots = 0

Sum of zeroes = -9

Product of zeroes = 20

x^{2} - (-9) x + 20 = 0

x^{2} + 9x + 20 = 0

Hence the required quadratic equation is x^{2} + 9x + 20 = 0.

(ii) 5/3, 4

Solution :

x^{2} - (sum of roots) x + product of roots = 0

Sum of zeroes = 5/3

Product of zeroes = 4

x^{2} - (5/3) x + 4 = 0

(3x^{2} - 5x + 4)/3 = 0

3x^{2} - 5x + 4 = 0

Hence the required quadratic equation is 3x^{2} - 5x + 4 = 0

(iii) -3/2, -1

Solution :

x^{2} - (sum of roots) x + product of roots = 0

Sum of zeroes = -3/2

Product of zeroes = -1

x^{2} - (-3/2) x + (-1) = 0

x^{2} + (3/2)x - 1 = 0

2x^{2} + 3x - 1 = 0

Hence the required quadratic equation is 2x^{2} + 3x - 1 = 0

(iv) -(2-a)^{2}, (a + 5)^{2}

Solution :

x^{2} - (sum of roots) x + product of roots = 0

Sum of zeroes = -(2-a)^{2}

Product of zeroes = (a + 5)^{2}

x^{2} - [-(2 - a)^{2} x] + (a + 5)^{2} = 0

x^{2} + (2 - a)^{2} x + (a + 5)^{2} = 0

Hence the required quadratic equation is x^{2} + (2 - a)^{2} x + (a + 5)^{2} = 0

After having gone through the stuff given above, we hope that the students would have understood, "How to Find the Quadratic Equation with the Sum and Product of Roots".

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