For what value of p does the quadratic x^2-2px+p+2=0 have exactly one solution?

1 Answer
Alan P.
Feb 18, 2016

p=-1 or p=2

Explanation:

The roots of a quadratic ax^2+bx+c=0 are equal when the discriminant (b^2-4ac) is equal to 0

In this case
color(white)("XXX")a=1
color(white)("XXX")b=-2p
color(white)("XXX")c=(p+2)

So the discriminant is
color(white)("XXX")(-2p)^2-4(1)(p+2)
color(white)("XXX")=4p^2-4p-8
which factors as
color(white)("XXX")=4(p-2)(p+1)

and the discriminant =0 if
color(white)("XXX")p=2 or p=-1

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