Chapter A.6, Problem 128AYU

To determine

To find: Whether each quadratic equation has two unequal real solutions, a repeated real solution, or no real solution without solving the equation: $2x^2-3x-4=0$.

Answer to Problem 128AYU

Two unequal real solutions.

Explanation of Solution

$2x^2-3x-4=0$

$a{x}^2+ bx + c = 0$ Compare to standard form.

With $a=2, b=-3$, and $c=-4$, the discriminant is $b^2-4ac={\left(-3\right)}^2-4\left(2\right)\left(-4\right)=41$.

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