Find the x-intercepts of the function.
-$f ( x ) = x ^ { 5 } \left( x ^ { 2 } - 25 \right) \left( x ^ { 2 } + 16 \right)$
A)x-intercept: (0, 0), x-intercept: (-5, 0)
B)x-intercept: (0, 0), x-intercept: (5, 0), x-intercept: (-5, 0)x-intercept: (4, 0), x-intercept: (-4, 0)
C)x-intercept: (0, 0), x-intercept: (5, 0)
D)x-intercept: (0, 0), x-intercept: (5, 0), x-intercept: (-5, 0)

Question

Quizplus · Accepted Answer

The x-intercepts occur where the function equals zero. The function is zero when $x^5 = 0$, $x^2 - 25 = 0$, or $x^2 + 16 = 0$. Solving these gives x-intercepts at $x = 0$, $x = 5$, and $x = -5$. The equation $x^2 + 16 = 0$ has no real solutions.

Find the X-Intercepts of the Function f(x)=x5(x2−25)(x2+16)f ( x ) = x ^ { 5 } \left( x ^ { 2 } - 25 \right) \left( x ^ { 2 } + 16 \right)f(x)=x5(x2−25)(x2+16)

Find the X-Intercepts of the Function $f ( x ) = x ^ { 5 } \left( x ^ { 2 } - 25 \right) \left( x ^ { 2 } + 16 \right)$