# Mat/117 DQ1

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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.

• Mat/117 DQ1 -

You can tell by the discriminant

a x^2 + b x + c = 0
look at
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
for example
(x-1)(x-2) = 0 two real x = 1 or 2
x^2 -3 x + 2 = 0

for example
(x-2)(x-2)
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

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