the polynomial of degree 3, P(x), has a root of multiplicity 2 at x=4 and a root of multiplicity 1 at x=-3. The y-intercept is y= -19.2 . Find a formula for P(x) .

Guest May 19, 2015

#1**+5 **

P(x) = (x -4)^2 (x +3) = x^3 - 5x^2 - 8x + 48

If the y intercept = -19.2 we need to solve 48m = -19.2 and m = (-2/5)...so....

P(x) = m ( x^3 - 5x^2 - 8x + 48) = (-2/5)x^3 + 2x^2 + (16/5)x - 19.2

Here's the graph........https://www.desmos.com/calculator/toyzyhqsgb

CPhill
May 19, 2015

#1**+5 **

Best Answer

P(x) = (x -4)^2 (x +3) = x^3 - 5x^2 - 8x + 48

If the y intercept = -19.2 we need to solve 48m = -19.2 and m = (-2/5)...so....

P(x) = m ( x^3 - 5x^2 - 8x + 48) = (-2/5)x^3 + 2x^2 + (16/5)x - 19.2

Here's the graph........https://www.desmos.com/calculator/toyzyhqsgb

CPhill
May 19, 2015