Question

the sum of the zeroes of quadratic polynomial is 5 and the sum of their square is 21 so find the quadratic polynomial

Answer 1

Step-by-step explanation:

Let a,b be the zeros of the polynomial. Then,

a+b= 8 and ab = k

Given,

a²+ b² = 40

(a + b)² - 2ab = 40

642k 40

2k = 24

k = 12

Answer 2

Step-by-step explanation:

Consider the zeros as α and β

==> α + β = 5

==> α² + β² = 21

==> (α + β)² – 2αβ = 21

==> (5)² – 2αβ = 21

==> 25 – 2ab = 21

==> 25 – 21 = 2ab

==> 4 = 2ab

==> 2 = ab

Product of zeros is 2.

Polynomial required is :

x² - (Sum of roots)x + Product of roots

==> x² – (α + β)x + αβ

==> x² – 5x + 2

Polynomial is x² – 5x + 2.