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ALGEBRA 2 help please;Question in the attached

ALGEBRA 2 help please;Question in the attached-example-1
User Imanol
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1 Answer

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Answer:


f(x) = x^(5) -3x^(2) -2 has 5 real and 0 non-real zeroes.

Explanation:

Here, the given polynomial is
f(x) = x^(5) -3x^(2) -2

Now, by FUNDAMENTAL THEOREM OF ALGEBRA:

A polynomial of degree n can have at most n roots.

So, here the number of roots f(x) can have = 5

Now, examine the change in the sign of f(x) and f(-x)


f(x) = x^(5) -3x^(2) -2

Signs of f(x) is + - -.

So for f(x) the sign changes only once.

Now,
f(-x) = (-x)^(5) -3(-x)^(2) -2

or,
f(-x) = -x^(5) -3x^(2) -2

Here, signs are - - -

So,for f(-x) the SIGNS DO NOT CHANGE.

So it has no negative real zero.

Hence,
f(x) = x^(5) -3x^(2) -2 has 5 real and 0 non-real zeroes.

User Harsh Nagalla
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