Question

find the value of k such that the expression is a perfect square trinomial 4x^2-6x+k
Can someone show me how to do it using complete the square or anyway how to do it?

Answer 1

Why do you want to do it using completed square? Tbh I can't even see how to do it that way.

We want to find a and b such that \[(ax+b)^2=(ax)^2+2abx+b^2=4x^2-6x+k\]We know \[(ax)^2=4x^2, a=2\]We also know\[2abx=2\times2bx=4bx-6x, b=-1.5\]So \[k=b^2=(-1.5)^2=2.25\]

Answer 2

would substituting the numbers in the equation b^2-4ac=0 work? I got the same answer from doing that.

Answer 3

Yep that would also work as it's a repeated root so the discriminant is equal to 0. Nice job, hadn't thought about it that way.