Question

If f(x) = x^2 - 5x + c, for which values of c will f(x) have zero real roots?

Answer 1

For any `c` greater than `25/4`.

Explanation:

A quadratic equation `ax^2+bx+c` has no real roots if its discriminant is strictly negative, where its discriminant is

`Delta = b^2-4ac`.

In your case, `a=1`, `b=-5` and `c` is to be found. So,

`Delta=5^2-4*1*c=25-4c`

We want `25-4c<0`, so `25<4c`. Solving for `c`, we get

`c>25/4`