How many solutions does #-x^2+5x+1=0# have?

1 Answer
Nov 12, 2016

Answer:

There are 2 solutions.

Explanation:

You can check the nature of the roots (solutions) without actually finding them.

Use #Delta = +-sqrt(b^2 -4ac)" "# from #" "ax^2 +bx+c =0#

For #" "-x^2 +5x+1 =0#

#Delta =+-sqrt( (5)^2 -4(-1)(1))#
#= +-sqrt(25+4)#
#=+-sqrt29#

This indicates that there are 2 solutions.

(they exist, so they are Real but Irrational)

(note: usually working with #-x^2 +5x+1 =0# is not very comfortable, but because it is an equation, it can be changed to
#x^2 -5x-1 =0# by multiplying by #-1#

(This does not change the outcome for the solutions.)