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 $G(x) = x^4 - 23x^2 - 50$, we can treat it as a quadratic equation in terms of $x^2$. Let $y = x^2$, then the equation becomes $y^2 - 23y - 50 = 0$. Factoring or using the quadratic formula, we find the roots of this equation to be $y = 25$ and $y = -2$. Since $y = x^2$, and $x^2$ cannot be negative for real numbers, we discard $y = -2$ and only consider $y = 25$, which gives $x^2 = 25$. Therefore, $x = \pm 5$, which are the real zeros of the function and also the x-intercepts of its 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 $G ( x ) = x ^ { 4 } - 23 x ^ { 2 } - 50$