Asked by candy
Why are there always at least two solutions in quadratic equations?
Answers
Answered by
drwls
The number of solutions is not "at least" two. There is always two OR ONE solutions, but they may not be real numbers. The solutions may contain a term multiplied by the square root of a negative number, which is "imaginary".
The reason for two solutions can be seen by looking at the "quadratic formula" for solutions:
(1/2a)[-b +/- sqrt(b^2 - 4ac)]
The two soltions are a result of the +/- term. When b^2 - 4ac equals zero, there is only one solution.
a,b and c are the coefficients in the standard form of a quadratic equation,
ax^2 + bx + c = 0
The reason for two solutions can be seen by looking at the "quadratic formula" for solutions:
(1/2a)[-b +/- sqrt(b^2 - 4ac)]
The two soltions are a result of the +/- term. When b^2 - 4ac equals zero, there is only one solution.
a,b and c are the coefficients in the standard form of a quadratic equation,
ax^2 + bx + c = 0
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