Solution assignment 08 Quadratic equations (abc-formula)

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Assignment 8

For which value(s) of p does the equation:

x^2-2x+p=0

have two different solutions x.

Solution

In order to find out whether a quadratic equation has two different solutions, one (or two coinciding) solution or no (real) solution at all, we have to look at the discriminant. In this case we have:

D=(-2)^2-4\cdot1\cdot{p}=4-4p

If the equation must have two different solutions the discriminant has to satisfy:

4-4p>0

or:

p<1

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