Find the real zeros of the function. List the x-intercepts of the graph of the function.
-$$P ( x ) = ( 4 x - 6 ) ^ { 2 } - 6 ( 4 x - 6 ) + 5$$
A) $x = - \frac { 7 } { 4 } , x = - \frac { 11 } { 4 }$
B) $x = \frac { 7 } { 4 } , x = \frac { 11 } { 4 }$
C) $x = \frac { 5 } { 4 } , x = - \frac { 1 } { 4 }$
D) $x = - \frac { 5 } { 6 } , x = \frac { 1 } { 4 }$

Question

Quizplus · Accepted Answer

The correct answer is B because the real zeros of the function are the x-intercepts of the graph of the function. To find the x-intercepts, set P(x) = 0 and solve for x.$$(4x-6)^2-6(4x-6)+5=0$$$$(4x-6)(4x-6-6)+5=0$$$$(4x-6)(4x-12)+5=0$$$$16x^2-48x-24x+72+5=0$$$$16x^2-72x+77=0$$$$(4x-11)(4x-7)=0$$$$4x-11=0 \quad \text{or} \quad 4x-7=0$$$$4x=11 \quad \text{or} \quad 4x=7$$$$x=\frac{11}{4} \quad \text{or} \quad x=\frac{7}{4}$$Therefore, the x-intercepts of the graph of the function are $x = \frac{7}{4}$ and $x = \frac{11}{4}$.

Find the Real Zeros of the Function P(x)=(4x−6)2−6(4x−6)+5P ( x ) = ( 4 x - 6 ) ^ { 2 } - 6 ( 4 x - 6 ) + 5P(x)=(4x−6)2−6(4x−6)+5

Find the Real Zeros of the Function $P ( x ) = ( 4 x - 6 ) ^ { 2 } - 6 ( 4 x - 6 ) + 5$