question please ?

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?

Answer 1

You look at the discriminant.
The discriminant of the equation ax^2 + bx + c = 0 is b^2 -4ac.

Case 1: If b^2 -4ac > 0, then there are two real and unequal roots.
Case 2: If b^2 - 4ac = 0, then there are two equal roots (some people may just say one real root).
Case 3: If b^2 - 4ac < 0, then there are two complex roots (if you are only looking for real roots, then this case would result in no solution).

For any quadratic equation, there are always two roots (real & unequal, real & equal, complex).

Answer 2

a quadratic equation has at most 2 solutions, say a and b
the formula for the quadratic equation is then
(x - a)*( x - b) = 0

like wise one solution : (x-a)(x-a) = 0

.

general equaltion is
ax^2 + bx + c = 0.
if the determinant < 0 no solutions
determinant = 0 one solution
de3terminant > 0 2 solutions.

determinant is : b^2 - 4*a*c.

Answer 3

ax^2+bx+c=0
x= -b+/-Sqrt(b^2-4ac)

if the Sqrt part is zero ...coincident roots (one solution)

if the sqrt part is negative ...then they are no real roots
(roots are complex or imaginary)

solution
x=0.5
x=-3

then those two answers came from

(2x-1)=0
(x+3)=0

so the quadractic was (2x-1)(x+3)

or 2x^2+5x-3