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

Algebra ->  Quadratic Equations and Parabolas -> 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      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
Use the discriminant.
D=b%5E2-4ac
If D%3E0, two real solutions.
If D=0, one real solutions.
If D%3C0, two complex solutions.
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If the solutions are a and b, then
f%28x%29=%28x-a%29%28x-b%29
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Yes, but they are only different by a constant multiplier.
f%28x%29=5%28x-2%29%28x-1%29
and
f%28x%29=12%28x-2%29%28x-1%29 both has x=1 and x=2 but only differ by the constant multiplier in front.
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Answer by richard1234(7193) About Me  (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.