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

Oct 16, 2015

For any $c$ greater than $\frac{25}{4}$.

#### Explanation:

A quadratic equation $a {x}^{2} + b x + c$ has no real roots if its discriminant is strictly negative, where its discriminant is

$\Delta = {b}^{2} - 4 a c$.

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

$\Delta = {5}^{2} - 4 \cdot 1 \cdot c = 25 - 4 c$

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

$c > \frac{25}{4}$