Question

How many x-intercepts appear on the graph of this polynomial function?
f(x)= x4-5x2​

Answer 1

1 x-intercepts

Explanation:

has same question on a test

Answer 2

The x-intercepts appear on this polynomial are 3 x intercepts.

Explanation:

To find the x intercepts of the polynomial
`f(x)=x^(4) -5x^(2)` is by equating
`f(x)=0`

Thus, the equation becomes

`\begin{array}{r}{x^(4)-5 x^(2)=0} \\{x^(2)\left(x^(2)-5\right)=0}\end{array}`

Equating, we get,

`x^(2)=0,\left(x^(2)-5\right)=0`

`x=0`,
`\begin{aligned}x^(2)-5 &=0 \\x^(2) &=5 \\x &=\pm √(5)\end{aligned}`

Thus, the x-intercepts are
`x=0, x=√(5) , x=-√(5)`

Hence, the x-intercepts appear on this polynomial are 3 x intercepts.