Answer
Zeros: $\dfrac{4}{3}, -\dfrac{5}{2}$
$x$-intercepts: $\dfrac{4}{3}, -\dfrac{5}{2}$
Work Step by Step
To find the zeros of a function $f$, solve the equation $f(x)=0$
The zeros of the function are also the $x-$intercepts.
Let $f(x)=0$:
$$6x^2+7x-20=0$$
Comparing $6x^2+7x-20=0$ to $ax^2+bx+c=0$ to find $a,b \text{ and } c$
$$\therefore a = 6, b=7 , c =-20$$
Evaluating the discriminant $b^2-4ac$
$$b^2-4ac = (7)^2-4 \times 6 \times -20 = 529$$
The quadratic formula is given by:
$$x= \dfrac{-b \pm \sqrt{b^2-4ac}}{2a}$$
$$x= \dfrac{-7\pm \sqrt{529}}{2\times 6}$$
$$x=\dfrac{-7\pm 23}{12}$$
Thus, the zeros, which are also the $x$-intercepts, are $\dfrac{4}{3}$ and $-\dfrac{5}{2}$.
