power functions and polynomial functions

Question

g is a polynomial of degree 3. g has a root of multiplicity 2 at c=5, g(−1)=0, and g(0)=−9.25. Find an algebraic equation for g.

Kyle L. · Accepted Answer

the values given to us in the expression tell us that the factored form would be

g(x) = a * (x-5)^2 (x+1)

because 5 is a root of multiplicity 2 and -1 is a root of multiplicity 1

the last step then is to plug in the point in order to solve for the coefficient value:

-9.25 = a * (-5)^2 * 1

-9.25 = 25a

a = -9.25 / 25 = -0.37

putting it all together gives

g(x) = -0.37(x – 5)^2(x + 1)

1 Expert Answer