SOLUTION: quadratic equations, which are expressed in the form of ax^2 + bx + c=0, where a does not equal 0, may have how many solutions? explain why.

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Question 444397: quadratic equations, which are expressed in the form of ax^2 + bx + c=0, where a does not equal 0, may have how many solutions? explain why.
Answer by poliphob3.14(115) About Me  (Show Source):
You can put this solution on YOUR website!
To find the solutions of quadratic equation ax%5E2%2Bbx%2Bc=0 where a≠0, we
divide both sides by a:%28x%5E2%2B%28b%2Fa%29x+%2Bc%2Fa%29=0, complete the square:
%28x%5E2%2B%28b%2Fa%29x%2Bb%5E2%2F4a%5E2%29=b%5E2%2F4a%5E2-c%2Fa => %28x%2Bb%2F2a%29%5E2=%28b%5E2-4ac%29%2F4a%5E2
Based on square root definition we have:x=%28-b+%2B-+sqrt%28b%5E2-4ac%29%29%2F2a
If b%5E2-4ac=0 we have one solution:x=-b%2F2a.
If b%5E2-4ac≠0 we have two different solutions:
x%5B1%5D=%28-b%2Bsqrt%28b%5E2-4ac%29%29%2F2a and x%5B2%5D=%28-b-sqrt%28b%5E2-4ac%29%29%2F2a
If b%5E2-4ac%3C0 the equation has no real solutions.