SOLUTION: Information is given about a polynomial f left parenthesis x right parenthesis whose coefficients are real numbers. Find the remaining zeros of f. Degree​ 4; ​ zeros: i, -13

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Information is given about a polynomial f left parenthesis x right parenthesis whose coefficients are real numbers. Find the remaining zeros of f. Degree​ 4; ​ zeros: i, -13      Log On


   

Question 1151677: Information is given about a polynomial f left parenthesis x right parenthesis whose coefficients are real numbers. Find the remaining zeros of f.
Degree​ 4; ​ zeros: i, -13+1
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
Degree​ 4; ​ => means there is 4 zeros
zeros: x%5B1%5D=i, => complex zeros come in pairs, so you also have x%5B2%5D=-i
-13+1 ? I guess here are two zeros, 13+and 1
so, x%5B3%5D=13, x%5B4%5D=1
f%28x%29=%28x-x%5B1%5D%29%28x-x%5B2%5D%29%28x-x%5B3%5D%29%28x-x%5B4%5D%29.....plug in given zeros
f%28x%29=%28x-i%29%28x-%28-i%29%29%28x-13%29%28x-1%29
f%28x%29=%28x-i%29%28x%2Bi%29%28x-13%29%28x-1%29
f%28x%29=%28x%5E2-i%5E2%29%28x-13%29%28x-1%29......since i%5E2=-1, we have
f%28x%29=%28x%5E2-%28-1%29%29%28x-13%29%28x-1%29
f%28x%29=%28x%5E2%2B1%29%28x-13%29%28x-1%29.......multiply all
f%28x%29=x%5E4-14x%5E3+%2B14x%5E2+-14x+%2B+13

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