Find a polynomial function F(x) of degree three with real coefficients that satisfies the following conditions. Zero of zero and zero of three have been multiplicity 2 ; f(4)=20

Answer 1

Hi Vivian C.,

Really, you should be able to set up this function at this semester point in a calculus course?

Roots imply a factor of (x-root) in the polynomial expression. Multiplicity of k means that a root is repeated, in the sense that the polynomial expression has that (x-root) factor repeated k times.

So far that gives f(x) = (x)(x-3)(x-3). Note that that expression is already degree 3, and is (almost) completely specified! However, although you cannot just add a constant to get up to f(x)=20 for x=4 (or it would not have zeros as stated), you can use a different mathematical operation with a constant. Because the function was stated to be a polynomial, that limits you to just one mathematical operation and constant (otherwise, you could use, say, an exponent to achieve f(x)=20). Hint: the constant to use is 5.

-- Cheers, --Mr. d.