Question

Find the quadratic Polynomials sum of whose
zeros is 8 and there product is 12 , Hence
find the zeros of the polynomials.​

Answer 1

Hello Ramji !

Answer:

Roots : (2,6)

x² - 8x + 12 = 0

Step-by-step explanation:

Given :

Sum of zeroes = 8

=> a + b = 8

Product of zeroes = 12

=> ab = 12

To find :

Quadratic Polynomial

Zeroes of the Polynomial

Procedure :

a + b = 8

=> a = 8 - b

Substitute this in ab = 12 :

=> (8 - b)(b) = 12

=> 8b - b² = 12

=> b² - 8b + 12 = 0

-6, -2 add up to -8, and product Is +12.

=> b² - 6b - 2b + 12 = 0

=> b(b - 6) - 2(b - 6) = 0

=> (b - 2)(b - 6) = 0

Hence b = 2 or 6.

If b = 2, a = 6

If b = 6, a = 2

Hence the zeroes are (2,6).

The quadratic equation when the roots a,b are given is :

x² - (a + b)x + ab = 0

=> x² - 8x + 12 = 0

Thanks !