posted by Rose on .
How do you know if a quadratic equation will have one, two, or no solutions?Please give examples. How do you find a quadratic equation if you are only given the solution? Please give an example.Is it possible to have different quadratic equations with the same solution? Explain and please give example. Provide your classmate’s with one or two solutions with which they must create a quadratic equation.
You can tell by the discriminant
a x^2 + b x + c = 0
b^2 - 4 ac
If positive, then two real solutions
If zero, then vertex on x axis and both solutions are the same
If negative, then no real solutions, solutions are complex numbers
for the rest, work up from factors
(x-1)(x-2) = 0 two real x = 1 or 2
x^2 -3 x + 2 = 0
x^2 - 4 x + 4 = 0 one solution (or two both the same)
(x-i)(x+i) = 0
x^2 - i^2 = x^2+1 = 0 no real solutions