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

x2 - (sum of roots) x + product of roots = 0

(or)

x2 - (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 :

x2 - (sum of roots) x + product of roots = 0

Sum of zeroes  =  -9

Product of zeroes  =  20

x2 - (-9) x + 20 = 0

x2 + 9x + 20 = 0

Hence the required quadratic equation is x2 + 9x + 20 = 0.

(ii)  5/3, 4

Solution :

x2 - (sum of roots) x + product of roots = 0

Sum of zeroes  =  5/3

Product of zeroes  =  4

x2 - (5/3) x + 4 = 0

(3x2 - 5x + 4)/3 = 0

3x2 - 5x + 4 = 0

Hence the required quadratic equation is 3x2 - 5x + 4 = 0

(iii)  -3/2, -1

Solution :

x2 - (sum of roots) x + product of roots = 0

Sum of zeroes  =  -3/2

Product of zeroes  =  -1

x2 - (-3/2) x + (-1) = 0

x2 + (3/2)x - 1 = 0

2x2 + 3x - 1 = 0

Hence the required quadratic equation is 2x2 + 3x - 1 = 0

(iv)  -(2-a)2, (a + 5)2

Solution :

x2 - (sum of roots) x + product of roots = 0

Sum of zeroes  =  -(2-a)2

Product of zeroes  =  (a + 5)2

x2 - [-(2 - a)2 x] + (a + 5)2 = 0

x2 + (2 - a)2 x + (a + 5)2 = 0

Hence the required quadratic equation is x2 + (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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