# Constucting cubic function from given complex zeros.

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• Feb 21st 2011, 01:36 AM
Barney
Constucting cubic function from given complex zeros.
Hi, The question is Write down a polynomial of degree 3, whose coefficients are all real, that has 4i and 2 as two of its zeros.

please help can you try to solve this. i got no clue(Headbang)
• Feb 21st 2011, 01:58 AM
joll
If you are asked to write down , for example, a polynominal of degree 2 that has 2 and 3 as its zeros, you will find;
f(x) = (x-2)(x-3)
by substituting either x=2 or x=3, it's clear this satisfies the question.

Similarly,....

+ if an polynominal f(x)=0 <whose coefficient is all real> has an complex root, x = a+bi, (a and b are real), we can say...
• Feb 21st 2011, 02:02 AM
earboth
Quote:

Originally Posted by Barney
Hi, The question is Write down a polynomial of degree 3, whose coefficients are all real, that has 4i and 2 as two of its zeros.

please help can you try to solve this. i got no clue(Headbang)

1. Let x denote the variable.

2. If x = 4i is a solution then x = -4i must be a solution too, otherwise all coefficient can't be real.

3. Now you can calculate the LHS of the equation:

$(x-2)(x-4i)(x+4i)=0$

4. Expand the LHS. Collect like terms. That's all.