math (precalc)
posted by Kyle .
Find a polynomial with integer coefficients that satisfies the given conditions.
R has degree 4 and zeros 3 − 4i and 5, with 5 a zero of multiplicity 2.

math (precalc) 
John1
x = 3  4i
x = 3 + 4i
x = 5
x =5
two 5's because multiplicity 2
You always have to have the conjugate of an imaginary number.
(x (34i))(x(3+4i)(x5)(x5) = 0
Easiest way is to multiply the first two and the second two factors.
Then multiply those answers together to get the polynomial. 
math (precalc) 
Anonymous
(x5)(x5)(x3+4i)(x34i) = 0
(x^210x+25)(x^26x+25)
multiply that out 
math (precalc) 
Steve
complex values come in pairs (why?), so the roots are
34i, 3+4i, 5, 5
R(x) = (x(34i))(x(3+4i))(x5)^2
= ((x3)+4i)((x3)4i)(x5)^2
= ((x3)^2+4^2)(x5)^2
= (x^26x+25)(x5)^2
= x^4  16x^3 + 110x^2  400x + 625
Respond to this Question
Similar Questions

Math Help Please
Suppose that a polynomial function of degree 5 with rational coefficients has 0 (with multiplicity 2), 3, and 1 –2i as zeros. Find the remaining zero. A. –2 B. –1 – 2i C. 0 D. 1 + 2i 
Algebra
Suppose that a polynomial function of degree 5 with rational coefficients has 0 (with multiplicity 2), 6, and –2 + 3i as zeros. Find the remaining zero. A. –6 B. –2 – 3i C. 0 D. 2 + 3i 
Pre Calculus
1. Find all rational zeros of the polynomial. Then determine any irrational zeros, and factor the polynomial completely. 3x^411x^3+5x^2+3x 2. Find the polynomial with leading coefficient 1 that has a degree of 4, a zero of multiplicity … 
college algebra
form a polynomial f(x) with real coefficients having the given degree and zeros degree 4 zeros 5+3i;3 multiplicity 2 enter the polynomial f(x)=a? 
algebra
form a polynomial f(x) with real coefficients having the given degree and zeros. Degree 4; zeros:3 +5i; 2 multiplicity 2 enter the polynomial f(x)=a(? 
calculusplease help!!
I have two questions that I don't understand and need help with. 1. information is given about a polynomial f(x) whose coefficients are real numbers. Find the remaining zerosof f. degree 4, zeros i;9+i 2. form a polynomial f(x) with … 
PreCalculus
Find a polynomial with integer coefficients that satisfies the given conditions. P has degree 2 and zeros 2 + i and 2 − i. 
Algebra ll
Please help!! I do not understand any of this!! Form a polynomial f(x) with real coefficients having the given degree and zeros. Degree 4; zeros: 2, multiplicity 2; 3i 
College Algebra
Find a fourthdegree polynomial with integer coefficients that has zeros 4i and −1, with −1 a zero of multiplicity 2. (Use x for the variable.) can somebody help me do this? 
PreCalc
Find a polynomial of the specified degree that satisfies the given conditions. Degree 4; zeros −3, 0, 1, 4; coefficient of x3 is 4