Question

Given that the quadratic equation hx^2 - 4kx + 9h =0 has two equal roots, find the ratio h:k

The answer given is 4:6. I need to know the method pls... Thx in advance

Answer 1

using the properties dealing with the nature of the roots,
if there are two equal roots, then b^2 - 4ac = 0
so in hx2 _ 4kx + 9h = 0
16k^2 -4(h)(9h) = 0
16k^2 = 36h^2
4k = 6h
h/k = 4/6

So h : k = 4 : 6 = 2 : 3

They should have reduced their answer to 2:3