If alpha and beta are zeros of a polynomial f(x)=x squared -6x+k find value of k such that alpha squared + beta squared =40

Answer 1

let's call the roots a and b, just for ease of typing.

f(x) = x^2-6x+k

recall the sum and product of the roots:

a+b = 6
ab = k

Now, we have

a^2 + b^2 = 40
but,
a^2 + b^2 = (a+b)^2 - 2ab

So,

36 - 2k = 40