SOLUTION: How do you know if a quadratic equation will have one, two, or no solutions? How do you find a quadratic equation if you are only given the solution? Is it possible to have differe

Question 379391: How do you know if a quadratic equation will have one, two, or no solutions? How do you find a quadratic equation if you are only given the solution? Is it possible to have different quadratic equations with the same solution? Explain. Provide your classmate�s with one or two solutions with which they must create a quadratic equation.

Found 2 solutions by Fombitz, richard1234:
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
Use the discriminant.

If , two real solutions.
If , one real solutions.
If , two complex solutions.
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.
.
If the solutions are and , then

.
.
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Yes, but they are only different by a constant multiplier.

and
both has and but only differ by the constant multiplier in front.
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.
.

Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
All quadratics have two solutions in the complex plane (including multiplicities). However, you can determine how many (real) solutions a quadratic has by looking at the discriminant (b^2 - 4ac). If the discriminant is positive, the quadratic has two real solutions; if it is zero, the quadratic has one double root, and if it is negative, the quadratic has two complex roots.
Also, a quadratic is uniquely determined by its roots. A quadratic with roots r_1 and r_2 must be in the form (x - r_1)(x - r_2) = 0, or x^2 - (r_1 + r_2)x + r_1r_2 = 0.
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