Chapter A.6, Problem 127AYU

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: $3x^2+5x-8=0$.

Answer to Problem 127AYU

Two unequal real solutions.

Explanation of Solution

$3x^2+5x-8=0$

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

With $a=3, b=5$, and $c=-8$, the discriminant is $b^2-4ac={\left(5\right)}^2-4\left(3\right)\left(-8\right)=121$.

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