SOLUTION: Find the equation of the polynomial with roots (-square root of 3, 0) and (4i, 0) real coefficients, and passing through the point (1 ,34)

Algebra ->  Equations -> SOLUTION: Find the equation of the polynomial with roots (-square root of 3, 0) and (4i, 0) real coefficients, and passing through the point (1 ,34)      Log On


   



Question 1198684: Find the equation of the polynomial with roots (-square root of 3, 0) and (4i, 0) real coefficients, and passing through the point (1 ,34)
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
given:
roots (-sqrt+%283%29, 0)=>then you also have (sqrt+%283%29,+0)
(4i, 0)=>then you also have (-4i,+0)
point (1 ,34)

f%28x%29+=+a+%28+x%5E2+-+3+%29%28+x%5E2+%2B+16%29
f%28x%29+=+a+%28+x%5E4+%2B+13x%5E2+-+48%29
use given point (1 ,34) to find a
34+=+a+%28+1%5E4+%2B+13%2A1%5E2+-+48%29
34+=+a+%28+-34%29
a+=+34%2F%28+-34%29
a+=+-1
f%28x%29+=-1+%28+x%5E4+%2B+13x%5E2+-+48%29
f%28x%29+=-x%5E4+-+13x%5E2+%2B+48=>answer