How many x intercepts appear on the graph of this polynomial function? f(x)=x^4-5x^2 1 x intercept 2 x intercepts 3 x intercepts 4 x intercepts

You can find the number of x intercepts by setting f(x) equal to zero giving you 0=x^4-5x^2. You can factor out an x^2 and divide on both sides (when you divide 0 by anything it is still zero so the x^2 disappears), and you are left with 0=x^2-5, which you can solve easily giving you x=+/- sqrt(5). However, the original equation also has an x intercept at (0,0) which you can see by plugging 0 in for x. So the grand total of x intercepts is 3!

aksnkj aksnkj · Answer 2 · 2022-02-14T09:42:03+01:00

There is a total of 3 x-intercepts that appear on the graph of this polynomial function.

Given:

[tex]\rm f(x)=x^4-5x^2\\\\1x- intercept\\\\2x-intercept\\\\3x-intercept[/tex]

According to the given function, we will solve the equation

How to find x and y-intercepts?

We can find the number of x-intercepts by setting

[tex]\rm f(x) =0 \\ 0=x^4-5x^2.[/tex]

We can factorise an [tex]\rm x^{2}[/tex] and then divide on both the sides we are left with [tex]\rm 0=x^2-5[/tex],

which can be solved easily by giving you [tex]\rm x=\pm \sqrt(5)[/tex].

However, the natural equation has an x-intercept at (0,0) which we can check by simplifying 0 for x.

Therefore, The grand total of x-intercepts is 3.

Learn more about Intercepts here:

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