Question

For the following equation, state the value of the discriminant and then describe the nature of the solutions, -9x^2+5x-12=0

Answer 1

The discriminant is the argument under the square root sign of the quadratic formula. In this case:\[\sqrt{b^2-4ac}=\sqrt{(5)^2-4(-9)(-12)}=\sqrt{25-432}=\sqrt{-407}\]No real solutions because we can't take the square root of a negative number

Answer 2

Could it have two imaginary solutions

Answer 3

In a quadratic equation \[ax ^{2} + bx + c = 0 \]
The discriminant is
\[\sqrt{b ^{2} - 4ac}\]

If the discriminant is a positive number there are 2 distinct (different) solutions. If it's 0 then there are 2 identical solutions. (ie, it's the minimum or maximum point of the curve) and if it's negative there are no real solutions.

Also, it would have 2 imaginary solutions. They would be conjugate pairs.