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

1 Answer
EZ as pi
Nov 12, 2016

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.)

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