How to use the discriminant to find out what type of solutions the equation has for #x^2 + 6x + 5 = 0#?

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Answer 1 · 2015-05-18T21:42:32

#x^2+6x+5# is of the form #ax^2+bx+c# with #a=1#, #b=6# and #c=5#.

The discriminant is given by the formula:

#Delta = b^2-4ac = 6^2-(4xx1xx5) = 36-20 = 16 = 4^2#

Since #Delta > 0#, the quadratic equation #x^2+6x+5 = 0# has two distinct real roots.

Further, since #Delta = 4^2# is a perfect square the roots are rational.

(In fact the solutions are given by the formula:

#x = (-b+-sqrt(Delta))/(2a) = (-6+-4)/2 = -3+--2#

That is #x = -1# or #x = -5#.)