# How do you find the discriminant x^2+x-12?

May 3, 2016

49

#### Explanation:

Given a quadratic equation in standard form $a {x}^{2} + b x + c = 0$

Then the discriminant $\textcolor{red}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{\left(\Delta\right) = {b}^{2} - 4 a c} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

The value of the discriminant gives information on the $\textcolor{b l u e}{\text{ nature of the roots }}$

• b^2-4ac > 0 " roots are real and irrational "

However if ${b}^{2} - 4 a c \text{ is a square , roots are real and rational}$

• b^2-4ac=0 " roots are real and equal "

• b^2-4ac < " roots are not real "

For the given function here ${x}^{2} + x - 12 , a = 1 , b = 1 , c = - 12$

$\Rightarrow {b}^{2} - 4 a c = {1}^{2} - \left(4 \times 1 \times - 12\right) = 49$

Since ${b}^{2} - 4 a c > 0 \text{ and a square , roots will be real and rational}$