Question

if alpha and beta are the zeroes of the polynomial f(x)=x^2-6x+k, then find the value of k, such that apha^2+ beta^2= 40

Answer 1

Answer:

Step-by-step explanation:

Given alpha and beta are the roots of the equation

So α+β= -(b) /a =6----(1)

αβ.=c/a = k---(2)

Given α^2+.β^2=40---(3)

.α+β=6

(α+β)^2=6^2

Expand

α^2+β^2+2αβ=36

Substitute (2) and (3)

40+2k=36

2k=36-40

2k=-4

K = -2

Answer is k= -2