Answer
$m = -1$ or $m = -\frac{3}{2}$
Work Step by Step
Use the Quadratic Formula $x = \dfrac{-b \pm \sqrt {b^2 - 4ac}}{2a}$, where $a$ is the coefficient of the $x^2$-term, $b$ is the coefficient of the $x$-term, and $c$ is the constant term.
The given trinomial has $a=2, b=5, c=3$ so substitute these values into the formula above to obtain:
$m = \dfrac{-5 \pm \sqrt {5^2 - 4(2)(3)}}{2(2)}$
Evaluate the exponent first:
$m = \dfrac{-5 \pm \sqrt {25 - 4(2)(3)}}{2(2)}$
$m = \dfrac{-5 \pm \sqrt {25 - 24}}{4}$
$m = \dfrac{-5 \pm \sqrt {1}}{4}$
$m = \dfrac{-5 ± 1}{4}$
Add or subtract terms in the numerator:
$m = \frac{-4}{4}$ or $m = \frac{-6}{4}$
Simplify the fractions:
$m = -1$ or $m = -\frac{3}{2}$
