SOLUTION: If x=3 or -4 are the solutions of the equation x^2+ax+b=0. Find the value of a and b.

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Question 1058046: If x=3 or -4 are the solutions of the equation x^2+ax+b=0. Find the value of a and b.

Found 2 solutions by solve_for_x, ikleyn:
Answer by solve_for_x(190) About Me  (Show Source):
You can put this solution on YOUR website!
Substituting x = 3 in the equation gives:

9 + 3a + b = 0

Then substituting x = -4 into the equation gives:

16 - 4a + b = 0

Subtracting the first equation from the second gives:

(16 - 9) + (-4a - 3a) + (b - b) = 0

7 - 7a = 0

7a = 7

a = 1

Substituting a = 1 into 9 + 3a + b = 0 then gives:

9 + 3(1) + b = 0

12 + b = 0

b = -12

Solution: a = 1, b = -12

Answer by ikleyn(52865) About Me  (Show Source):
You can put this solution on YOUR website!
.
If x=3 or -4 are the solutions of the equation x^2+ax+b=0. Find the value of a and b.
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Then a = -(3+(-4)) = -(-1) = 1

and

b = 3*(-4) = -12.

See the lesson
    - https://www.algebra.com/algebra/homework/quadratic/lessons/Solving-quadratic-equations-without-quadratic-formula.lesson
in this site.

Vieta's formulas.