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
:
Illustrated by the graph

RELATED QUESTIONS
How do you know if a quadratic equation will have one, two, or no solutions? (answered by richwmiller)

how do you know if a quadratic equation will have one, two or no solutions? If only given (answered by stanbon)

How do you know if a quadratic equation will have one, two, or no... (answered by richard1234)

How do you know if a quadratic equation will have one, two, or no solutions? How do you... (answered by jsmallt9,solver91311)

How do you know if a quadratic equation will have one, two, or no solutions? How do you... (answered by Alan3354)

How do you know if a quadratic equation will have one, two, or no solutions? How do you... (answered by solver91311)

How do you know if a quadratic equation will have one, two, or no solutions? How do you... (answered by Fombitz,richard1234)

How do you know if a quadratic equation will have one, two, or no solutions? How do you... (answered by richwmiller)

This is one main question with several parts. Please help. Thank you, How do you know if (answered by vleith,solver91311,Alan3354)

How do you know if a quadratic equation will have one, two, or no solutions? How do you... (answered by stanbon)