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 268002: 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 Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! How do you know if a quadratic equation will have one,two, or no solutions?
You use the discriminant rules
In the form ax^2 + bx + c, the discriminant: D = -b^2 - 4*a*c
If D > 0 we have two real number solutions that are not equal
If D = 0 we have one real solution (a double root)
If D < 0 we have two complex (non-real) number solutions
:
how do you find a quadratic equation if you are only given the solution?
An example would be easy to understand. Say we have two solutions (roots)
x = 7, x = -3
They can be derived from the factors
(x-7)(x+3) = 0
FOIL
x^2 + 3x - 7x - 21 = 0
y = x^2 - 4x - 21 would be the equation
:
Is it possible to have different quadratic equations with the same solution?
Yes, the equation y = -x^2 + 4x + 21 will have the same solutions as the one above altho the vertex value of y will be different
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Illustrated by the graph
