Question

If p, q are zeroes of polynomial f(x) = 2x^2– 7x + 3 , find the value of p^2 + d^2

Answer 1

Answer:

37/4

Step-by-step explanation:

Given polynomial f(x) = 2x² - 7x + 3

let, f(x) = 2x² - 7x + 3 = 0

⇒2x² - 7x + 3 = 0      (∵ the factors of ‘+6’ to get their sum as -7 is -6 & -1)

by factorisation method,

⇒ 2x² - 6x - x + 3 = 0

⇒ 2x(x - 3) - (x - 3) = 0

⇒ (2x-1)(x-3) = 0

case-(1):                         Case-(2):

             2x-1 = 0                          x-3 = 0

          ⇒2x = 1                            ⇒ x = 3

           ⇒ x = 1/2

given the zeroes of the polynomial are p,q

so, let

⇒ p = 1/2 & q = 3

now,

p² + q² = (1/2)² + (3)²

⇒ p² + q² = (1/4) + (9)

take LCM,

⇒ p² + q² = (1+36)/4

⇒ p² + q² = 37/4

∴ p²+q² = 37/4

HOPE THIS WOULD BE HELPFUL FOR YOU