SOLUTION: 1.Given that f(x) is a cubic function with zeros at -3, 0, and 6, find an equation for f(x) given that f(8) = 9. f(x)=__________ 2. Suppose p(x) is a polynomial with real coeffici

Question 996805: 1.Given that f(x) is a cubic function with zeros at -3, 0, and 6, find an equation for f(x) given that f(8) = 9. f(x)=__________
2. Suppose p(x) is a polynomial with real coefficients that bounces off the x-axis at 47, bounces off the x-axis at -28, and breaks through the x-axis at 91. If p(-9-7i)=p(-6+4i)=0. what is the smallest possible degree that p(x) could have?

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
f(x)=a(x+3)(x)(x-6)=a(x^3-3x^2-18x)
f(8)=9, so (8,9) is a point
9=a(x^3-3x^2-18x)
9=a(512-192-144)
9=176a
a=(9/176)
(9/176)(x^3-3x^2-18x)

=======================
Complex roots are conjugate.
2 complex roots, so 4 altogether there.
2 bounces, so that is 4 more at least.
1 crossing.
degree 9 minimal.

RELATED QUESTIONS
Given that f(x) is a cubic function with zeros at -6,-2 , and 6, find an equation for... (answered by stanbon)

Given that f(x) is a cubic function with zeros at -2 and 2 i - 1 , find an equation for... (answered by josgarithmetic)

given that f(x) is a cubic function with zeros at -5 and -4i +3, find an equation for... (answered by ikleyn)

given that f(x) is a cubic function with zeros at -5 and -4i +3, find an equation for... (answered by josgarithmetic,ikleyn)

Given that f(x) is a cubic function with zeros at −6, 0, and 4, find an equation for... (answered by ikleyn,MathLover1,Solver92311)

If f is a linear function, f(0.1) = 9.3, and f(0.4) = −6.3, find an equation f(x)... (answered by CubeyThePenguin)

Given the polynomial function f(x),find the rational zeros,then the other zeros(that... (answered by lwsshak3)

Suppose that f is a linear function with slope -3.2 and that f(1) = 8. What value of x... (answered by ikleyn)

The function f, defined for x ∈ R, x>0, is such that: f'(x) =x^2 - 2+x^-2 Given... (answered by Fombitz)