Find the real zeros of the function. List the x-intercepts of the graph of the function.
-$$G ( x ) = x ^ { 4 } - 23 x ^ { 2 } - 50$$
A) $x = - 5 , x = 5$
B) $x = - 25 , x = 2$
C) $x = - \sqrt { 2 } , x = \sqrt { 2 }$
D) no real solution

Question

Quizplus · Accepted Answer

To find the real zeros of the function, we can factor the given equation. Let $y = x^2$, then the equation becomes $y^2 - 23y - 50 = 0$. Factoring this quadratic equation, we get $(y - 25)(y + 2) = 0$, which gives $y = 25$ and $y = -2$. Since $y = x^2$, we have $x^2 = 25$ and $x^2 = -2$. The equation $x^2 = 25$ has real solutions $x = 5$ and $x = -5$, while $x^2 = -2$ has no real solutions. Therefore, the real zeros of the function are $x = -5$ and $x = 5$, which are also the x-intercepts of the graph.

Find the Real Zeros of the Function G(x)=x4−23x2−50G ( x ) = x ^ { 4 } - 23 x ^ { 2 } - 50G(x)=x4−23x2−50

Find the Real Zeros of the Function $G ( x ) = x ^ { 4 } - 23 x ^ { 2 } - 50$