Find the real zeros of the function. List the x-intercepts of the graph of the function.
-$$P ( x ) = ( 2 x - 5 ) ^ { 2 } - 8 ( 2 x - 5 ) + 12$$
A) $x = - \frac { 1 } { 5 } , x = \frac { 3 } { 2 }$
B) $x = - \frac { 11 } { 2 } , x = - \frac { 7 } { 2 }$
C) $x = \frac { 11 } { 2 } , x = \frac { 7 } { 2 }$
D) $x = \frac { 1 } { 2 } , x = - \frac { 3 } { 2 }$

Question

Quizplus · Accepted Answer

The function can be rewritten as a quadratic in terms of $u = 2x - 5$. Solving the quadratic equation $u^2 - 8u + 12 = 0$ gives $u = 6$ or $u = 2$. Substituting back for $x$, we get $2x - 5 = 6$ or $2x - 5 = 2$, leading to $x = \frac{11}{2}$ or $x = \frac{7}{2}$.

Find the Real Zeros of the Function P(x)=(2x−5)2−8(2x−5)+12P ( x ) = ( 2 x - 5 ) ^ { 2 } - 8 ( 2 x - 5 ) + 12P(x)=(2x−5)2−8(2x−5)+12

Find the Real Zeros of the Function $P ( x ) = ( 2 x - 5 ) ^ { 2 } - 8 ( 2 x - 5 ) + 12$