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

1 Answer
May 18, 2015

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.)