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. Provide your
classmate’s with one or two solutions with which they must create a quadratic equation.
2 answers
So what is your thinking? We will be happy to critique your thinking.
Usually a quadratic equation will be squared but it depends on the power of x.
b^2 - 4ac (the discrimant) determines number of solutions.
if > 0, 2 solutions
if = 0, 1 solution (a double solution)
if < 0, 0 (real) solutions (but 2 imaginary)
Given solutions x = 2, x = -4; equation is:
(x-2)(x+4) = 0 or x^2 + 2x - 8 = 0
Different equations only in the sense they are a multiple of the original one. x^2 + 3x + 5 = 0 and
2x^2 + 6x + 10 = 0 are multiples of each onther and have the same solutions.
b^2 - 4ac (the discrimant) determines number of solutions.
if > 0, 2 solutions
if = 0, 1 solution (a double solution)
if < 0, 0 (real) solutions (but 2 imaginary)
Given solutions x = 2, x = -4; equation is:
(x-2)(x+4) = 0 or x^2 + 2x - 8 = 0
Different equations only in the sense they are a multiple of the original one. x^2 + 3x + 5 = 0 and
2x^2 + 6x + 10 = 0 are multiples of each onther and have the same solutions.
1 answer