SOLUTION: which quadratic equations has roots of -3 and 2?

Algebra ->  Radicals -> SOLUTION: which quadratic equations has roots of -3 and 2?       Log On


   

Question 1156388: which quadratic equations has roots of -3 and 2?

Found 3 solutions by MathLover1, ikleyn, Theo:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
roots of x%5B1%5D=-3 and x%5B2%5D=2


f%28x%29=%28x-x%5B1%5D%29%28x-x%5B2%5D%29
f%28x%29=%28x-%28-3%29%29%28x-2%29
f%28x%29=%28x%2B3%29%28x-2%29
f%28x%29=x%5E2-2x%2B3x-6
f%28x%29=x%5E2%2Bx-6

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E2%2Bx-6%29+

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.

Any quadratic equation of the form


   a*(x-(-3))*(x-2) = 0,


which is the same as 


    a*(x+3)*(x-2) = 0,


where "a" is any non-zero real number.


There are INFINITELY MANY such equations.


And they ALL are EQUIVALENT, i.e. have the same set of solutions.


Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
the roots are -3 and 2
set x = -3
add 3 to both sides of that equation to get x + 3 = 0
that's one of your factors.
set x = 2
subtract 2 from both both sides of that equation to get x - 2 = 0
that's your other factor.
your factors are (x + 3) * (x - 2) = 0
simplify that equation to get x^2 - 2x + 3x - 6 = 0
combine like terms to get x^2 + x - 6 = 0
the graph of that equation looks like this.

$$$