Question

What value of k is the expression x^4+kx^2+36 a perfect square?

Answer 1

`\text{ The discriminant is 0 if the quadratic expression is a perfect square.}\\\\~~~~~b^2 -4ac =0\\\\\implies k^2-4\cdot 1 \cdot 36 = 0\\ \\\implies k^2 - 144 = 0\\\\\implies k^2 = 144\\\\\implies k = \pm√(144)\\\\\implies k= \pm12\\\\\text{Hence}~ k=12 ~\text{and}~ k=-12.`