Question 39
The polynomial of degree $5, P(x)$ has leading coefficient 1 , has roots of multiplicity 2 at $x=3$ and $x=0$ , and a root of multiplicity 1 at $x=-5$
Find a possible formula for $P(x)$.
\[
P(x)=
\]
Question Help: $\square$ Video

Answer

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Answer

$\boxed{P(x) = x^5 - x^4 - 21x^3 + 45x^2}$ is the possible formula for the polynomial.

Steps

Step 1 ：Given that the polynomial has roots of multiplicity 2 at x=3 and x=0, and a root of multiplicity 1 at x=-5, we can write the polynomial as: $P(x) = (x-3)^2 * (x-0)^2 * (x+5)$

Step 2 ：Expanding this expression, we get $P(x) = x^5 - x^4 - 21x^3 + 45x^2$

Step 3 ：$\boxed{P(x) = x^5 - x^4 - 21x^3 + 45x^2}$ is the possible formula for the polynomial.

Question 39The polynomial of degree $5, P(x)$ has leading coefficient 1 , has roots of multiplicity 2 at $x=3$ and $x=0$ , and a root of multiplicity 1 at $x=-5$Find a possible formula for $P(x)$.\[P(x)=\]Question Help: $\square$ Video

Answer

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Question 39
The polynomial of degree $5, P(x)$ has leading coefficient 1 , has roots of multiplicity 2 at $x=3$ and $x=0$ , and a root of multiplicity 1 at $x=-5$
Find a possible formula for $P(x)$.
\[
P(x)=
\]
Question Help: $\square$ Video