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

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

Question 1 :

-9 and 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

Question 2 :

5/3 and 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

Question 3 :

-3/2 and -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

Question 4 :

-(2-a)² and (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

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