SOLUTION: Find an nth degree polynomial function with real coefficients satisfying the given conditions.
n=3;-5 and i are zeros; f(-3)=60
Algebra.Com
Question 1057890: Find an nth degree polynomial function with real coefficients satisfying the given conditions.
n=3;-5 and i are zeros; f(-3)=60
Answer by solve_for_x(190) (Show Source): You can put this solution on YOUR website!
Since i is a zero, -i is also a zero, because imaginary roots always occur in conjugate pairs.
The factors of the desired polynomial are then (x - 5), (x - i), and (x + i).
The function is then:
f(x) = a(x - 5)(x - i)(x + i)
f(x) = a(x - 5)(x^2 - i^2)
f(x) = a(x - 5)(x^2 + 1)
f(x) = a(x^3 - 5x^2 + x - 5)
Then:
f(-3) = a((-3)^3 - 5(-3)^2 + (-3) - 5) = 60
a(-27 - 45 - 3 - 5) = 60
a(-80) = 60
a = -60/80
a = -3/4
The function is then:
RELATED QUESTIONS
find an nth degree polynomial function with real coefficients satisfying the given... (answered by RAY100)
Find an nth degree polynomial function with real coefficients satisfying the given... (answered by Fombitz)
Find an nth degree polynomial function with real coefficients satisfying the given... (answered by stanbon)
Find an nth-degree polynomial function with real coefficients satisfying the given (answered by MathLover1)
Find an nth- degree polynomial function with real coefficients satisfying the given... (answered by greenestamps)
Find an nth degree polynomial function with real coefficients satisfying the given... (answered by josgarithmetic)
Find an nth-degree polynomial function with real coefficients satisfying the given (answered by Fombitz)
find an nth degree polynomial function with real coefficients satisfying the given... (answered by greenestamps)
find an nth degree polynomial function with real coefficients satisfying the given... (answered by drk)