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motikmotik
3 years ago
7

The polynomial of degree 3, P(x), has a root of multiplicity 2 at x=5 and a root of multiplicity 1 at x=−5.

Mathematics
1 answer:
satela [25.4K]3 years ago
3 0

Answer:

P(x) = -0.7(x-5)^{2}(x+5)

Step-by-step explanation:

Root multiplicity of 2 means the root is repeated 2 times. Root multiplicity of 1 means root is repeated only once.

A polynomial of degree 3 means the largest exponent of x is 3.

Here, the polynomial P(x) has root 5 with multiplicity 2 and -5 with multiplicity 1.

So, P(x) = a(x-5)^{2}(x+5)

Where, a is a constant.

Now, it's given that the y intercept is -87.5. Therefore, value of x at y intercept is 0.

We obtain a by plugging in -87.5 for P(x) and 0 for x.

-87.5=a(0-5)^{2}(0+5)

-87.5=a(25\times5)\\ a=-\frac{87.5}{125}=-0.7

Therefore, the polynomial P(x) is given as:

P(x) =-0.7(x-5)^{2}(x+5)

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