Question

I can't seem to figure out how to solve the question: Find the value of k greater than zero for x²-5k²x+4k² has equal roots.

Answer 1

In this polynomial, a = 1 ; b = -5k^2 ; c = k^2

As this has equal roots, so D = 0

⇒b^2 - 4ac = 0

⇒25k^4 - 16k^2 = 0

Either, k^2 = 0 ⇒ k = 0

or, 25k^2 - 16 = 0

⇒(5k - 6)(5k + 6) = 0

Either, k = 6/5   or, k = -6/5

A.T.Q. k>0

Therefore k = 6/5