SOLUTION: write each quadratic equation that has the given roots 1. 5+ 3 sqrt 2 and 5- 3 sqrt 2 2. 6+2i and 6-2i show all work

Algebra ->  Rational-functions -> SOLUTION: write each quadratic equation that has the given roots 1. 5+ 3 sqrt 2 and 5- 3 sqrt 2 2. 6+2i and 6-2i show all work      Log On


   



Question 927960: write each quadratic equation that has the given roots
1. 5+ 3 sqrt 2 and 5- 3 sqrt 2
2. 6+2i and 6-2i
show all work

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
using roots, we have
f%28x%29=%28x-x%5B1%5D%29%28x-x%5B2%5D%29
1.
if x%5B1%5D=5%2B+3sqrt%282%29 and x%5B2%5D=5-3sqrt%282%29,then we have
f%28x%29=%28x-x%5B1%5D%29%28x-x%5B2%5D%29
f%28x%29=%28x-%285%2B+3sqrt%282%29%29%29%28x-%285-3sqrt%282%29%29%29
f%28x%29=%28x-5-3sqrt%282%29%29%28x-5%2B3sqrt%282%29%29




f%28x%29=x%5E2-10x%2B25-18

f%28x%29=x%5E2-10x%2B7

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E2-10x%2B7%29+
2.
x%5B1%5D=6%2B2i and x%5B2%5D=6-2i

f%28x%29=%28x-x%5B1%5D%29%28x-x%5B2%5D%29

f%28x%29=%28x-%286%2B2i%29%29%28x-%286-2i%29%29
f%28x%29=%28x-6-2i%29%28x-6%2B2i%29
f%28x%29=x%5E2-6x%2B2xi-6x%2B36-12i-2ix%2B12i-4%28i%29%5E2+

f%28x%29=x%5E2-12x%2B36-4%28-1%29+
f%28x%29=x%5E2-12x%2B36%2B4+
f%28x%29=x%5E2-12x%2B40+

+graph%28+600%2C+600%2C+-10%2C+15%2C+-10%2C+50%2C+x%5E2-12x%2B40%29+