How to use the discriminant to find out how many real number roots an equation has for x^2+4x+5?

1 Answer
George C.
May 17, 2015

x^2+4x+5 is of the form ax^2+bx+c with a=1, b=4 and c=5.

The discriminant is given by the formula:

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

Since this is negative, x^2+4x+5=0 has no real roots. It has two distinct complex roots.

The various possible cases are:
Delta > 0 : The quadratic has two distinct real roots.
Delta = 0 : The quadratic has one repeated real root.
Delta < 0 : The quadratic has no real roots. It has two distinct complex roots.

In addition, if the original coefficients are integers (or rational numbers) and Delta >= 0 is a perfect square, then the roots are rational numbers.

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