SOLUTION: Quadratic Equations Write a quadratic equation with the given roots. a)5, and -2 b)-3 over 4, and -2 over 3

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Quadratic Equations Write a quadratic equation with the given roots. a)5, and -2 b)-3 over 4, and -2 over 3      Log On


   

Question 177834: Quadratic Equations
Write a quadratic equation with the given roots.
a)5, and -2
b)-3 over 4, and -2 over 3
Found 2 solutions by Mathtut, solver91311:
Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
I will do a) and let you do b)
:
We know that roots take the form of x-k=0 where k is a root
:
so (x-5)(x-(-2)=0
:
%28x-5%29%28x%2B2%29=0
:
x%5E2%2B2x-5x-10=0
:
highlight%28x%5E2-3x-10=0%29is our quadratic equation
:
now for b)
:
-3/4 is one root and -2/3 the other
:
so you would start out (x+(3/4))(x+(2/3)) and go from there

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!

a) Given roots are 5 and -2, therefore and

If , then

and

If , then

Now you have the two factors for your quadratic:



Using FOIL:



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Do the other one the same way. Hint: so so