Download How do you know if a quadratic equation will have one, two, or no

How do you know if a quadratic equation will have one, two, or no solutions?
A quadratic equation has the form ax2 + bx + c = 0. The “discriminant” of the
quadratic equation is equal to b2 – 4ac. The value of the discriminant tells you
how many solutions there are to the equation.
If the discriminant is positive, then the equation has two real solutions.
If the discriminant is zero, then the equation has one real solution.
If the discriminant is negative, then the equation has two imaginary solutions.
How do you find a quadratic equation if you are only given the solution?
If you only have the solutions to the quadratic equation, you can reconstruct
the equation in the following manner.
Suppose that “m” and “n” are the solutions. Write the equation:
(x – m)(x – n) = 0
and substitute the given values of the solutions “m” and “n”. Multiplying out
the two terms gives:
x2 – mx – nx + mn = 0
x2 – (m + n)x + mn = 0
If there is only one solution, then replace both “m” and “n” with that one value.
Is it possible to have different quadratic equations with the same solution? Explain.
Yes, it is possible to have different quadratic equations that have the same
solution, if one equation is a multiple of the other.
Provide your classmate’s with one or two solutions with which they must create a
quadratic equation.
Solutions: x = 5, x = -3
The quadratic equation for these solutions is:
(x – 5)(x – (-3)) = 0
(x – 5)(x + 3) = 0
x2 – 5x + 3x – 15 = 0
x2 – 2x – 15 = 0