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Can someone tell me how i find answer for this problem?

Can someone tell me how i find answer for this problem?-example-1
User Broesch
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1 Answer

2 votes

Answer:

P(x) = x²(x +1)(x -2)²

Explanation:

You want the 5th degree polynomial with leading coefficient 1 that has roots of 0 and 3, each with multiplicity 2, and a root of -1.

Factors

You recall that a polynomial with root p has (x -p) as a factor. A root that is repeated m times has multiplicity m.

You recall that an exponent is used to signify the number of times a factor is repeated.

The factored form of P(x) is then ...

P(x) = (x -2)²(x -0)²(x -(-1)) . . . . . roots 2 and 0 repeated twice, root -1

P(x) = x²(x +1)(x -2)²

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Additional comment

If you like, you can multiply it out and collect terms. The result will be ...

P(x) = x⁵ -3x⁴ +4x²

User Leeyuiwah
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