Question

What is the discriminant of `5x^2 + 10x + 5 = 0`?

Answer 1

The discriminant is zero

Explanation:

By definition, the discriminant is simply `b^2-4ac`, where `a`, `b` and `c` are coefficients of

`ax^2+bx+c`

So, in your case, `a=c=5` and `b=10`. Plug that values in the definition to have

`b^2-4ac = 10^2 - 4*5*5 = 100-100=0`

A discriminant is zero when the parabola is a perfect square, and indeed this is the case, since

`(sqrt(5)x+sqrt(5))^2 = 5x^2 + 2*sqrt(5)x*sqrt(5)+5 = 5x^2+10x+5`