Find the real zeros of the function. List the x-intercepts of the graph of the function.
-$$F ( x ) = x ^ { 4 } - 10 x ^ { 2 } + 9$$
A) $x = - 9 , x = 9$
B) $x = - 1 , x = 1 , x = - 3 , x = 3$
C) $x = - 3 , x = 3$
D) $x = - 10 , x = 10$

Question

Quizplus · Accepted Answer

To find the real zeros of the function $F(x) = x^4 - 10x^2 + 9$, we can set $F(x) = 0$ and solve for $x$. This gives us the equation $x^4 - 10x^2 + 9 = 0$. This can be seen as a quadratic equation in terms of $x^2$, where $x^2 = y$, leading to $y^2 - 10y + 9 = 0$. Solving this quadratic equation for $y$ (or $x^2$) gives $y = 1$ and $y = 9$, which means $x^2 = 1$ and $x^2 = 9$. Therefore, the solutions for $x$ are $x = \pm1$ and $x = \pm3$, corresponding to the x-intercepts of the graph of the function.

Find the Real Zeros of the Function F(x)=x4−10x2+9F ( x ) = x ^ { 4 } - 10 x ^ { 2 } + 9F(x)=x4−10x2+9

Find the Real Zeros of the Function $F ( x ) = x ^ { 4 } - 10 x ^ { 2 } + 9$