Question

Question:
Given that h and k are the roots of quadratic equation 5x^2-10x+2=0, find the value of h^2+k^2

I have used alpha + beta method to do but it not works

Answer 1

use the properties of sum and product of roots
sum of roots
= h+k
= 10/5 = 2
product of roots
= hk
= 2/5

we know:
(h+k)^2 = h^2 + k^2 + 2hk
2^2 = h^2+k^2 + 2(2/5)
h^2+k^2 = 4-4/5 = 16/5