Question

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?

Answer 1

We use discriminant to find it.

b^2 - 4ac
is the formula.

Answer 2

\[ax^2+bx+c=0\]if\[\Delta= b^2 - 4ac >0\] then it has 2 real solution
if \[\Delta=0\] then it has one solution it means roots are the same..(double roots)

Answer 3

if \[\Delta <0\]
then it has no real solution, it means it has complex solution..