# How do you find the value of the discriminant and determine the number of real-number solutions for this quadratic equation x^2-11x+30=0?

Nov 11, 2016

The solutions are $S = \left\{5 , 6\right\}$

#### Explanation:

The equation is ${x}^{2} - 11 x + 30$

The discriminant is $\Delta = {b}^{2} - 4 a c$
$= {\left(- 11\right)}^{2} - 4 \cdot 1 \cdot 30 = 121 - 120 = 1$

As, $\Delta > 0$, we would expect two real roots.

$x = \frac{- b \pm \sqrt{\Delta}}{2 a} = \frac{11 \pm 1}{2}$

So, ${x}_{1} = 6$ and ${x}_{2} = 5$