Find the real zeros of the function. List the x-intercepts of the graph of the function.
-$$G ( x ) = x ^ { 4 } - 19 x ^ { 2 } - 150$$
A) $x = - 5 , x = 5$
B) $x = - 25 , x = 6$
C) $x = - \sqrt { 6 } , x = \sqrt { 6 }$
D) no real solution

Question

Quizplus · Accepted Answer

To find the real zeros of the function $G(x) = x^4 - 19x^2 - 150$, we can treat it as a quadratic equation by substituting $y = x^2$, giving us $y^2 - 19y - 150 = 0$. Factoring or using the quadratic formula, we find $y = 25$ or $y = -6$. Since $y = x^2$, and $x^2$ cannot be negative for real numbers, we discard $y = -6$ and keep $y = 25$, which gives us $x^2 = 25$. Solving for $x$, we get $x = 5$ or $x = -5$, which are the real zeros of the function and thus the x-intercepts of its graph.

Find the Real Zeros of the Function G(x)=x4−19x2−150G ( x ) = x ^ { 4 } - 19 x ^ { 2 } - 150G(x)=x4−19x2−150

Find the Real Zeros of the Function $G ( x ) = x ^ { 4 } - 19 x ^ { 2 } - 150$