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

The function can be factorised to give x²(x²-5). Therefore the graph will touch the x axis at zero and cut it at -√5 and √5, giving three x-intercepts. To check, let's look at a graph my calculator drew of this function:

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frika frika · Answer 2 · 2018-08-22T17:42:41+02:00

frika frika

22-08-2018

From the diagram you can see that the graph of function has three x-intercepts. If you need the coordinates of these points, then you should substitute y=0 and solve the received equation:

[tex] 0=x^4-5x^2 [/tex].

First, factor this expression:

[tex] x^2(x^2-5)=0,\\x^2(x-\sqrt{5}) (x+\sqrt{5})=0 [/tex].

This means that

[tex] x_1=0, x_2=\sqrt{5} ,x_3=-\sqrt{5} [/tex].

The x-intercepts are points

[tex] (0,0), (\sqrt{5},0), (-\sqrt{5},0) [/tex].

Answer: 3 x-intercepts.

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