SOLUTION: write each quadratic equation that has the given roots. 1. -3 and 5 2. 1/2 and -4 3. sqrt5 and -sqrt5 4. 5+3 sqrt 2 and 5-3 sqrt 2 5. 6+2i and 6-2i show all work

Algebra ->  Rational-functions -> SOLUTION: write each quadratic equation that has the given roots. 1. -3 and 5 2. 1/2 and -4 3. sqrt5 and -sqrt5 4. 5+3 sqrt 2 and 5-3 sqrt 2 5. 6+2i and 6-2i show all work      Log On


   



Question 927924: write each quadratic equation that has the given roots.
1. -3 and 5
2. 1/2 and -4
3. sqrt5 and -sqrt5
4. 5+3 sqrt 2 and 5-3 sqrt 2
5. 6+2i and 6-2i
show all work

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
use formula:
f%28x%29=%28x-x%5B1%5D%29%28x-x%5B2%5D%29
1.
+x%5B1%5D=-3 and x%5B2%5D=5
f%28x%29=%28x-%28-3%29%29%28x-5%29
f%28x%29=%28x%2B3%29%28x-5%29
f%28x%29=x%5E2-5x%2B3x-15
f%28x%29=x%5E2-2x-15

2.
+x%5B1%5D=1%2F2 and +x%5B2%5D=-4+
f%28x%29=%28x-%281%2F2%29%29%28x-%28-4%29%29
f%28x%29=%28x-%281%2F2%29%29%28x%2B4%29
f%28x%29=x%5E2%2B4x-%281%2F2%29x-%281%2F2%294
f%28x%29=x%5E2%2B%288%2F2%29x-%281%2F2%29x-2
f%28x%29=x%5E2%2B%287%2F2%29x-2


3.
x%5B1%5D=sqrt%285%29 and x%5B2%5D=-sqrt%285%29
f%28x%29=%28x-x%5B1%5D%29%28x-x%5B2%5D%29
f%28x%29=%28x-sqrt%285%29%29%28x-%28-sqrt%285%29%29%29
f%28x%29=%28x-sqrt%285%29%29%28x%2Bsqrt%285%29%29


f%28x%29=x%5E2-5


4.
x%5B1%5D=5%2B3sqrt%282%29 and x%5B2%5D=5-3sqrt%282%29
f%28x%29=%28x-x%5B1%5D%29%28x-x%5B2%5D%29
f%28x%29=%28x-%285%2B3sqrt%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%5E2-5x-5x%2B25-9%2A2
f%28x%29=x%5E2-10x%2B25-18
f%28x%29=x%5E2-10x%2B7


5.
x%5B1%5D=6%2B2i and x%5B1%5D=6-2i+
f%28x%29=%28x+-+%286+%2B+2i%29%29%28x+-+%286+-+2i%29%29
f%28x%29=%28x-6-2i%29%28x-6%2B2i%29
f%28x%29=x%5E2-6x%2B2i%2Ax-6x%2B36-12i-2i%2Ax%2B12i-2i%282i%29+

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+