The polynomial of degree 3 , P ( x ) , has a root of multiplicity 2 at x = 1 and a root of multiplicity 1 at x = − 1 . The y -intercept is y = − 0.1 .

Question

The polynomial of degree , , has a root of multiplicity  at  and a root of multiplicity  at . The -intercept is .

Find a formula for 

Answer 1

Come on Cole C.,

You absolutely should be able to start to write the factored formula right out from the problem statement. If an equation has a ROOT, the polynomial of that equation has a factor of (x-ROOT). Always!!

Multiplicity means, there are more than one times that factor of (x-ROOT) appears in the factored equation (note the minus sign there: "root" means that when x=ROOT and you subtract ROOT, you end up with 0 for a factor, which multiplies through to 0 overall, so the polynomial is "ROOT"ed to the x-axis there -- it passes through the value 0).

So for the problem here, you write (x-1)*(x-1)*(x+1), that's x^3-x^2-x+1.

Now, as is, that polynomial has a value at x=0, namely 1. You can't just subtract 1.1 from the constant (that would throw the roots off!). But you CAN multiply the whole polynomial by a factor, to turn that 1 into a -0.1. I leave it up to you to determine and to apply that multiplier.

--Cheers, --Mr. d.