Question

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

Answer 1

The discriminant is `-1791`.

Explanation:

When an expression is given in standard form, `ax^2+bx+c`, the discriminant is simply `b^2-4ac`.

With this expression:

• `a=-21`
• `b=-15`
• `c=-24`

`\rightarrow b^2-4ac`

`\rightarrow (-15)^2-4(-21)(-24)`

`\rightarrow 225-2016`

`\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.