Find the real zeros of the function. List the x-intercepts of the graph of the function.
-$$F ( x ) = x ^ { 4 } - 26 x ^ { 2 } + 25$$
A) $x = - 5 , x = 5$
B) $x = - 26 , x = 26$
C) $x = - 25 , x = 25$
D) $x = - 1 , x = 1 , x = - 5 , x = 5$

Question

Quizplus · Accepted Answer

To find the real zeros of the function, we can factor the given equation: $F(x) = x^4 - 26x^2 + 25$. This can be factored as a quadratic in form by substituting $y = x^2$, giving us $y^2 - 26y + 25 = 0$. Factoring this quadratic equation, we get $(y - 1)(y - 25) = 0$, which gives us $y = 1$ and $y = 25$. Substituting back $x^2$ for $y$, we get $x^2 = 1$ and $x^2 = 25$, which gives us the real zeros $x = -1, x = 1, x = -5$, and $x = 5$. These are also the x-intercepts of the graph of the function.

Find the Real Zeros of the Function F(x)=x4−26x2+25F ( x ) = x ^ { 4 } - 26 x ^ { 2 } + 25F(x)=x4−26x2+25

Find the Real Zeros of the Function $F ( x ) = x ^ { 4 } - 26 x ^ { 2 } + 25$