# How do you find the discriminant of -21x ^ { 2} - 15x - 24?

Jan 25, 2018

The discriminant is $- 1791$.

#### Explanation:

When an expression is given in standard form, $a {x}^{2} + b x + c$, the discriminant is simply ${b}^{2} - 4 a c$.

With this expression:

• $a = - 21$
• $b = - 15$
• $c = - 24$

$\setminus \rightarrow {b}^{2} - 4 a c$

$\setminus \rightarrow {\left(- 15\right)}^{2} - 4 \left(- 21\right) \left(- 24\right)$

$\setminus \rightarrow 225 - 2016$

$\setminus \rightarrow - 1791$

Since the discriminant is negative, plugging the values of the above $a$, $b$, and $c$ into the quadratic equation will result in 0 real solutions.

There will be 2 imaginary solutions, though.