SOLUTION: I need help on this: Find a polynomial equation of lowest degree with integer coefficients and has 0,3, and also plus/minus square root of 2 as zeros.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I need help on this: Find a polynomial equation of lowest degree with integer coefficients and has 0,3, and also plus/minus square root of 2 as zeros.      Log On


   

Question 33693: I need help on this:
Find a polynomial equation of lowest degree with integer coefficients and has 0,3, and also plus/minus square root of 2 as zeros.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Since the required polynomial has 4 zeros (roots) it has to be a 4th degree polynomial.
If x = 0 is a root, then x is a factor.
If x = 3 is a root, then x - 3 is a factor.
If x = (+-)sqrt%282%29 are roots, then x%5E2+=+2 and x%5E2+-+2 is a factor.
Now we can get the equation by multiplying the known factors.
x%28x-3%29%28x%5E2-2%29+=+0
x%28x%5E3-3x%5E2-2x%2B6%29+=+0
x%5E4-3x%5E3-2x%5E2%2B6x+=+0