Find the real zeros of the function. List the x-intercepts of the graph of the function.
-$$Q ( x ) = ( - 5 x + 4 ) ^ { 2 } - 2 ( - 5 x + 4 ) - 24$$
A) $x = \frac { 8 } { 5 } , x = - \frac { 2 } { 5 }$
B) $x = - 4 , x = 6$
C) $x = - \frac { 8 } { 5 } , x = \frac { 2 } { 5 }$
D) $x = 0 , x = - 2$

Question

Quizplus · Accepted Answer

To find the real zeros of the function, we set $Q(x) = 0$ and solve for $x$. Let $u = -5x + 4$, then the equation becomes $u^2 - 2u - 24 = 0$. Factoring or using the quadratic formula, we find $u = -4$ or $u = 6$. Substituting back for $u$, we get $-5x + 4 = -4$ and $-5x + 4 = 6$. Solving these equations for $x$ gives $x = \frac{8}{5}$ and $x = -\frac{2}{5}$, respectively.

Find the Real Zeros of the Function Q(x)=(−5x+4)2−2(−5x+4)−24Q ( x ) = ( - 5 x + 4 ) ^ { 2 } - 2 ( - 5 x + 4 ) - 24Q(x)=(−5x+4)2−2(−5x+4)−24

Find the Real Zeros of the Function $Q ( x ) = ( - 5 x + 4 ) ^ { 2 } - 2 ( - 5 x + 4 ) - 24$