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

1 Answer
Feb 18, 2016

Answer:

#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#