SOLUTION: Find an equation for f(x), the polynomial of smallest degree with real coefficients such that f(x) bounces off of the x-axis at −5, breaks through the x-axis at −2, has

Question 1011139: Find an equation for f(x), the polynomial of smallest degree with real coefficients such that f(x) bounces off of the x-axis at −5, breaks through the x-axis at −2, has complex roots of −2+2i and −4−2i and passes through the point (0,−54).
Answer by josgarithmetic(39630) (Show Source): You can put this solution on YOUR website!
Real roots are -5 and -2;
Other complex roots are -2+2i, -2-2i, -4-2i, -4+2i.
Further, and you use the y-intercept to finally find a.

Start with .

----this really combined two steps including knowing about difference of squares and of i*i=-1;

--------at this stage, the function is in purely factored form without showing complex nor imaginary expressions - only real coefficients. You CAN still use this to find the value for a, making use of the given y-intercept; and you may still want to continue the full multiplication into general form.
RELATED QUESTIONS
Find an equation for f(x), the polynomial of smallest degree with real coefficients such (answered by stanbon)

1.Given that f(x) is a cubic function with zeros at -3, 0, and 6, find an equation for... (answered by Boreal)

Find an equation for f(x), the polynomial of smallest degree with real coefficients such (answered by Edwin McCravy,MathLover1,ikleyn,solver91311)

Find a polynomial f(x) of degree 3 with real coefficients and the following zeros.... (answered by solver91311)

Find a polynomial f(x) of degree 3 with real coefficients and the following zeros. -3,... (answered by aaronwiz)

Find a polynomial f(x) of degree 3 with real coefficients and the following zeros -4,1-i (answered by hkwu)

Form the third-degree polynomial function, f(x), with real coefficients such that 3i and... (answered by josgarithmetic)

Find a polynomial function f(x) of degree 3 with real coefficients that satisfies the... (answered by Fombitz)

SOLUTION: Find an equation for f(x), the polynomial of smallest degree with real coefficients such that f(x) bounces off of the x-axis at &#8722;5, breaks through the x-axis at &#8722;2, has

SOLUTION: Find an equation for f(x), the polynomial of smallest degree with real coefficients such that f(x) bounces off of the x-axis at −5, breaks through the x-axis at −2, has