SOLUTION: A polynomial f(x) with real coefficients and leading coefficient 1 has the given zeros and degree. Express f(x) as a product of linear and/or quadratic polynomials with real coeffi

Algebra ->  Inequalities -> SOLUTION: A polynomial f(x) with real coefficients and leading coefficient 1 has the given zeros and degree. Express f(x) as a product of linear and/or quadratic polynomials with real coeffi      Log On


   

Question 1171293: A polynomial f(x) with real coefficients and leading coefficient 1 has the given zeros and degree. Express f(x) as a product of linear and/or quadratic polynomials with real coefficients that are irreducible over ℝ.
−1, 0, 5 + i; degree 4
Found 2 solutions by MathLover1, DiamondYogi:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
given zeros:
x%5B1%5D=-1
x%5B2%5D=0
x%5B3%5D=5+%2B+i=> there is also x%5B4%5D=5-i (complex zeros always come in pairs)
f%28x%29=%28x-x%5B1%5D%29%28x-x%5B2%5D%29%28x-x%5B3%5D%29%28x-x%5B4%5D%29
f%28x%29=%28x-%28-1%29%29%28x-0%29%28x-%285%2Bi%29%29%28x-%285-i%29%29
f%28x%29=%28x%2B1%29%28x%29%28x-5-i%29%28x-5%2Bi%29

f%28x%29=%28x%5E2%2Bx%29%28x%5E2+-10x+%2B+26%29
f%28x%29=x%5E4+-+9x%5E3+%2B+16x%5E2+%2B+26x





Answer by DiamondYogi(1) About Me  (Show Source):