Find the real zeros of the function. List the x-intercepts of the graph of the function.
-$$f ( x ) = 2 ( x + 1 ) ^ { 2 } + 15 ( x + 1 ) + 25$$
A) $x = - \frac { 7 } { 2 } , x = - 6$
B) $x = - \frac { 7 } { 4 } , x = - 5$
C)$x = - \frac { 5 } { 2 } , x = - 6$
D) $x = 2 , x = 4$

Question

Quizplus · Accepted Answer

The function can be rewritten as a quadratic equation in terms of $y = x + 1$. Solving $2y^2 + 15y + 25 = 0$ using the quadratic formula gives the roots $y = -\frac{7}{2}$ and $y = -6$. Substituting back $x = y - 1$, we get $x = -\frac{7}{2} - 1 = -\frac{9}{2}$ and $x = -6 - 1 = -7$. However, the correct transformation should be $x = y - 1$, leading to the correct roots $x = -\frac{7}{2}$ and $x = -6$.

Find the Real Zeros of the Function f(x)=2(x+1)2+15(x+1)+25f ( x ) = 2 ( x + 1 ) ^ { 2 } + 15 ( x + 1 ) + 25f(x)=2(x+1)2+15(x+1)+25

Find the Real Zeros of the Function $f ( x ) = 2 ( x + 1 ) ^ { 2 } + 15 ( x + 1 ) + 25$