Question

plz answer problem no.5 in section 2

Answer 1

Hello friend !

The answer is given below:

Given quadratic equation  = x² - 8x + k , where a = 1 , b = -8 , c = k

Let the zeros of the polynomial be α and β 

Then, we know that 

⇒ αβ = $\frac{c}{a}$

⇒ αβ = k       (Equation 1)

⇒ α + β = $\frac{-b}{a}$

⇒ α + β = $- (\frac{-8}{1} )$ = 8

Squaring both the sides, we will get :

⇒ (α + β)² = 64

⇒ α² + β² + 2αβ = 64

Since α² + β² = 40 (given)

⇒ 40 + 2k = 64  (from equation 1)

⇒ 2k = 24

⇒ k = 12

This is your answer .

Hope this Helps !