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anonymous
 one year ago
Find a polynomial with integer coefficients that satisfy the given condition. R has degree 4 and zeros 12i and 1, with a zero of multiplicity 2.
anonymous
 one year ago
Find a polynomial with integer coefficients that satisfy the given condition. R has degree 4 and zeros 12i and 1, with a zero of multiplicity 2.

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mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1A zero of multiplicity 2 means there is one zero that appears twice.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Also, if a polynomial with integer coefficients has complex roots, then those roots must appear in pairs of complex conjugate roots.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1For example, if the polynomial has the root 3 + 5i, then it must also have 3  5i as a root.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i got everything it's just that i don't know how to multiply [x(1+2i)] with [x(12i)]

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1This is one way of doing it: First, simplify the parentheses inside each expression. Then multiply them together using polynomial multiplication. That is, multiply every term of the first polynomial by every term of the second polynomial, then collect like terms.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1The other way of doing it is to turn the product into the product of a sum and a difference and end up with the difference of two squares. Then you simplify.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Are you ok with this problem now? Do you need more help?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1\(\large y = [x(1+2i)][x(12i)](x  1)^2\)

campbell_st
 one year ago
Best ResponseYou've already chosen the best response.1looking at your complex zero you know \[x = 1 \pm 2i\] then rewriting you get \[x 1 = \pm 2i\] square both sides of the equation \[(x 1)^2 = 4i^2\] or \[(x 1)^2 = 4\] then you can find the quadratic factor

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Method 1: \(\large y = \color{red}{[x(1+2i)][x(12i)]}(x  1)^2\) \(\large y = \color{red}{(x1 2i)(x 1+2i)}(x  1)^2\) \(\large y = \color{red}{(x^2x + 2xi x +1 2i 2xi + 2i 4i^2)}(x  1)^2\) \(\large y = \color{red}{(x^22x +1+4)}(x  1)^2\) \(\large y = \color{red}{(x^22x +5)}(x  1)^2\) Method 2: \(\large y = \color{red}{[x(1+2i)][x(12i)]}(x  1)^2\) \(\large y = \color{red}{[(x1)2i][(x1)+2i]}(x  1)^2\) \(\large y = \color{red}{[(x1)^2(2i)^2]}(x  1)^2\) \(\large y = \color{red}{[x^2  2x + 1  (4)]}(x  1)^2\) \(\large y = \color{red}{(x^2  2x + 5)}(x  1)^2\) After doing the step above with either method 1 or method 2 or with @campbell_st 's method, you still need to square x  1, and then multiply it all together.
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