Question Proof By Induction (One Step)

Question

I'm self studying proof by induction and have a question about this one step for this question. I have attached the solution and question below.

How does one know that $kx^2\ge0$ ?

Thank you so much!

Answer 1

The proof is for all positive integers, so $k\ge0$ and $x^2\ge 0$ always since squaring a negative number gives you a positive number. Hence $kx^2$ is a product of non-negative numbers and hence is non-negative. That is, $kx^2\ge 0$.

Answer 2

You have $k\ge 0$ and the square of any real number is nonnegative, so $kx^2\ge 0$.