## Precalculus (10th Edition)

$x=\frac{1}{2}$ or $x=-4$
Equation:$2x^2+7x-4=0$ Factor the trinomial. The coefficient of $x^2$ is $2$, hence the coefficients of x in the multipliers are probably $2$ and $1$. The coefficient of $x^0$ (the constant) is $-4$, hence the possible coefficients of the $x^0$ are: $-2$ and $2$; or $-1$ and $4$; or $1$ and $-4$. Out of these combinations, the factors that give a middle term of $7x$ are $(2x-1)(x+4)=0$. Use the Zero-Product Property by equating each factor to zero, then solve each equation to obtain: \begin{align*} 2x-1&=0 &\text{or}& &x+4=0\\ 2x&=1 &\text{or}& &x=-4\\ x&=\frac{1}{2} &\text{or}& &x=-4 \end{align*}