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Solve the quadratic formula when a=5, b=12, and c=3 and also solve it with a=3, b=-5, and c=-9

I'm trying to solve the quadratic formula with these numbers, but my answers always ended up not being whole numbers. Can you solve it for me and tell me what you get? 

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quadratic equation:  a(x^2) + bx + c = 0

quadratic formula:  x = [-b +/-square_root(b^2 - 4ac)]/(2a)

so, that with a = 5; b = 12; c = 3;

we have: 

x = [-12 +/-square_root(12^2 - 4*5*3]/(2*5) 

   = [-12 +/-square_root(144-60)]/10

    = [-12 +/-square_root(84)]/10

similarly for a = 3; b = -5; and c = -9

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1 Answer

Phoebe,

Generally, the quadratic formula will not produce whole numbers.  In fact, that is the main advantage of the formula because it provides a way to "quickly" solve quadratic equations that cannot be factored because they lack whole number solutions.  Assuming the a,b, and c's you've provided are correct, those quadratics will not have whole number answers, so your computed answer is probably correct.

There are lots of quadratic solvers available to check your work.  I like

http://mathportal.org/calculators/solving-equations/quadratic-equation-solver.php

As it shows its steps as it goes through developing the solution, so you can see where you may have gone wrong.

I hope this helps.  John