Find the zeros of the function and state the multiplicities.
-$$f ( x ) = 4 x ^ { 4 } - 101 x ^ { 2 } + 25$$
A) $\frac { 1 } { 4 } , 25$; each of multiplicity 1
B) $- 5 , - \frac { 1 } { 2 } , \frac { 1 } { 2 } , 5$; each of multiplicity 1
C) $\frac { 1 } { 2 } , 5$; each of multiplicity 1
D) $- \frac { 1 } { 4 } , - 25$; each of multiplicity 1

Question

Quizplus · Accepted Answer

To find the zeros of the function $f(x) = 4x^4 - 101x^2 + 25$, we can treat it as a quadratic equation in terms of $x^2$. Let $y = x^2$, then the equation becomes $4y^2 - 101y + 25 = 0$. Solving this quadratic equation using the quadratic formula gives $y = \frac{101 \pm \sqrt{101^2 - 4(4)(25)}}{2(4)}$, which simplifies to $y = \frac{1}{4}$ and $y = 25$. Since $y = x^2$, we take the square root of each solution for $y$, yielding $x = \pm \frac{1}{2}$ and $x = \pm 5$. Therefore, the zeros of the function are $-5, -\frac{1}{2}, \frac{1}{2}, 5$, each with multiplicity 1.

Find the Zeros of the Function and State the Multiplicities f(x)=4x4−101x2+25f ( x ) = 4 x ^ { 4 } - 101 x ^ { 2 } + 25f(x)=4x4−101x2+25

Find the Zeros of the Function and State the Multiplicities $f ( x ) = 4 x ^ { 4 } - 101 x ^ { 2 } + 25$