Question

Find the discriminant of each quadratic equation, then state the number and type of solution:

-4n^2 - 7n - 5 = 0
6a^2 + 7a - 10 = 0
5p^2 + 6 = -2p
4x^2 - 8x = -5

Answer 1

The discriminant of a quadratic equation can be used to determine the number and type of solutions. A positive discriminant indicates two distinct real solutions, a zero discriminant indicates one real solution, and a negative discriminant indicates two complex solutions. By calculating the discriminant for each quadratic equation, we can determine the number and type of solutions for each equation.

Step-by-step explanation:

The discriminant of a quadratic equation can be found using the formula: discriminant = b^2 - 4ac.

To find the number and type of solutions, we look at the value of the discriminant:

• If the discriminant is positive, there are two distinct real solutions.
• If the discriminant is zero, there is one real solution.
• If the discriminant is negative, there are no real solutions, but there are two complex solutions.

Let's find the discriminant for each quadratic equation: