Find the real zeros, if any, of each quadratic function using the quadratic formula. List the x-intercepts, if any, of the
graph of the function.
-$$f ( x ) = 5 x ^ { 2 } - 28 x - 12$$
A) $x = - \frac { 2 } { 5 } , x = 6$
B) $x = - \frac { 4 } { 5 } , x = 12$
C) $x = - 2 , x = 6$
D) $x = \frac { 2 } { 5 } , x = - 6$

Question

Quizplus · Accepted Answer

The quadratic formula is $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$, where $a = 5$, $b = -28$, and $c = -12$. Plugging these values in gives $x = \frac{28 \pm \sqrt{(-28)^2 - 4(5)(-12)}}{2(5)}$, which simplifies to $x = \frac{28 \pm \sqrt{784 + 240}}{10}$ or $x = \frac{28 \pm \sqrt{1024}}{10}$, leading to $x = \frac{28 \pm 32}{10}$. Thus, the solutions are $x = \frac{60}{10} = 6$ and $x = \frac{-4}{10} = -\frac{2}{5}$, which are the x-intercepts.

Find the Real Zeros, If Any, of Each Quadratic Function f(x)=5x2−28x−12f ( x ) = 5 x ^ { 2 } - 28 x - 12f(x)=5x2−28x−12

Find the Real Zeros, If Any, of Each Quadratic Function $f ( x ) = 5 x ^ { 2 } - 28 x - 12$