Question

if alpha and beta are the zeroes of the polynomial f(x)=x2-6x+k find the value of k, such that alpha square + beta square =40

Answer 1

f(x)= x²-6x+k

Let alpha and beta are the zeroes of the quadratic polynomial f(x).

Now,
alpha ²+beta²= 40 -----------(i)

Therefore, alpha +beta= -b/a= -(-6)/1

= alpha + beta = 6 -------------(ii)

& alpha × beta= c/a= k/1

= alpha × beta= k ---------------(iii)

So from (i) ,

alpha² + beta²= 40

(alpha+beta)²- 2 alpha× beta= 40

(6)² - 2× k= 40

36-2k= 40

-2k= 40-36

-2k= 4

k= -4/2

Therefore, k= -2

Hope it helps you buddy.

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