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

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

Found 3 solutions by MathLover1, ikleyn, Theo:
Answer by MathLover1(20849)   (Show Source): You can put this solution on YOUR website!
roots of and










Answer by ikleyn(52781)   (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)   (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.

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