When p is false and q is true, then p or q is truesometimesalwaysnever

Ответ:

Heneyda

04.03.2020

ANSWER

The zeros are x=-5,x=0,x=5

EXPLANATION

Given;

f(x)=x^4-25x^2 .

We can rewrite the function as

f(x)=x^2(x^2-25)

$\Rightarrow f(x)=x^2(x^2-5^2)$

$\Rightarrow f(x)=x^2(x-5)(x+5)$

The zeros are found by equating the function to zero.

$\Rightarrow x^2(x-5)(x+5)=0$

$\Rightarrow (x-5)=0$

The multiplicity is 1, since it is odd the graph crosses at this intercept. which is x=5

$\Rightarrow (x+5)=0$

The multiplicity is 1, since it is odd the graph crosses at this intercept. which is x=-5

$\Rightarrow x^2=0$

This last root has a multiplicity of 2.

That is

x=0 repeats two times.

Since the multiplicity is even, the graph touches the x-axis at the point x=0 .

See graph.

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