Chapter A.6, Problem 145AYU

To determine

To find: The benefits of evaluating the discriminant of a quadratic equation before attempting to solve it.

Answer to Problem 145AYU

Discriminant of a Quadratic Equation is $b^2-4ac$ for a quadratic equation $a{x}^2 + bx + c = 0$.

1. If $b^2-4ac>0$, there are two unequal real solutions.

2. If $b^2-4ac=0$, there is a repeated real solution, a root of multiplicity 2.

3. If $b^2-4ac<0$, there is no real solution.

Discriminant of a Quadratic Equation gives what type of solution we get from the quadratic equation.

Explanation of Solution

Discriminant of a Quadratic Equation is $b^2-4ac$ for a quadratic equation $a{x}^2 + bx + c = 0$.

1. If $b^2-4ac>0$, there are two unequal real solutions.

2. If $b^2-4ac=0$, there is a repeated real solution, a root of multiplicity 2.

3. If $b^2-4ac<0$, there is no real solution.

Discriminant of a Quadratic Equation gives what type of solution we get from the quadratic equation.