SOLUTION: find the equation for p p is a degree 5 polynomial that passes through the origin, has zeros i and 4−i, and p(5)=520

Algebra.Com
Question 1161068: find the equation for p p is a degree 5 polynomial that passes through the origin, has zeros i and 4−i, and p(5)=520
Found 3 solutions by greenestamps, MathLover1, ikleyn:
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


The graph passing through the origin means one root is 0; the polynomial has a factor of x.

A zero of i means a zero of -i. The quadratic factor producing those two roots is

A zero of 4-i means a zero of 4+1. The quadratic factor producing those two roots is

The polynomial is



The constant a is determined by the requirement that p(5) = 520.





The polynomial function is




Answer by MathLover1(20849)   (Show Source): You can put this solution on YOUR website!

given:
is a degree

has zeros :
-> complex zeros always come in pair, so you also have

, and also

passes through the origin: point (,)-> 5th root is


use zero product rule:
....substitute given zeros


......since we are given, use it to find




and your equation is




Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.

As the problem is presented in the post, it is a FAULT,

since the post does not state that the polynomial is with real coefficients.


At the university, where I studied Math, for such formulation the student could deserve only lowest possible score.

It only means that the person who created it, does not know Math and does not know this subject, in particular.




RELATED QUESTIONS

q is a degree 5 polynomial that passes through the origin, has zeros i and 7−i, and (answered by ikleyn)
Find a polynomial with integer coefficients that satisfies the given conditions. P has... (answered by Alan3354)
for the following, find the function P defined by a polynomial of degree 3 with real... (answered by ewatrrr)
Please help and show all work. Thanks Real Zeros of Polynomials 1.... (answered by KMST)
Find a polynomial with integer coefficients that satisfies the given conditions. P has... (answered by Fombitz)
P has degree 3 and zeros 2 and i. find a polynomial that satisfies the given conditions.... (answered by Fombitz)
Please help me I am so lost. Please show all steps and work. Thanks Real Zeros of... (answered by Alan3354,Theo)
The polynomial of degree 4, P(x) has roots of multiplicity 2 at x=4 and roots of... (answered by josgarithmetic)
For the​ following, find the function P defined by a polynomial of degree 3 with real... (answered by josgarithmetic)