SOLUTION: Given the zeros, 2-i, 1, 2, write a polynomial function of least degrees that has real coefficients, anda leading coefficient of 2. I know it starts out like::: 2(x-1)(x-2)

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: Given the zeros, 2-i, 1, 2, write a polynomial function of least degrees that has real coefficients, anda leading coefficient of 2. I know it starts out like::: 2(x-1)(x-2)       Log On


   

Question 63125: Given the zeros, 2-i, 1, 2, write a polynomial function of least degrees that has real coefficients, anda leading coefficient of 2.
I know it starts out like::: 2(x-1)(x-2)
But I get really confused on how to put the 2-i part in. I really would like your help, as my friends don't get it either.
Thank you very much,
E
Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
(x - (2 - i))(x - (2 + i))
((x - 2) - i)((x - 2) + i)
(x - 2)^2 - i^2
x^2 - 4x + 4 + 1
x^2 - 4x + 5
Check:
x+=+%28-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%284+%2B-+sqrt%28+16+-+20+%29%29%2F%282%29+
x+=+%284+%2B-+i%2Asqrt%28+4+%29%29%2F%282%29+
x+=+%284+%2B-+2i%29%2F%282%29+
x+=+2+%2B-+i+ Correct....
(x^2 - 4x + 5)(x - 1)(x - 2)
(x^2 - 4x + 5)(x^2 - 3x + 2)
x^4 - 4x^3 + 5x^2 - 3x^3 + 12x^2 - 15x + 2x^2 - 8x + 10
x^4 - 7x^3 + 19x^2 - 23x + 10
2x^4 - 14x^3 + 38x^2 - 46x + 20 = f(x)
graph%28400%2C400%2C-10%2C10%2C-10%2C10%2C2x%5E4+-+14x%5E3+%2B+38x%5E2+-+46x+%2B+20%29