How do you use the discriminant to find the number of real solutions of the following quadratic equation: 2x^2 + 2x + 2 = 0?

1 Answer
George C.
Jul 4, 2015

2x^2+2x+2=0 has discriminant Delta = -12 which is negative. So there are no real solutions, only two distinct complex ones.

Explanation:

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

This has discriminant Delta given by the formula:

Delta = b^2-4ac = 2^2-(4xx2xx2) = 4 - 16 = -12

Since Delta < 0 there are no real solutions of 2x^2+2x+2=0. It has two distinct complex solutions.

The possibilities are:

Delta > 0 The quadratic has two distinct solutions. If Delta is a perfect square (and the coefficients of the quadratic are rational) then the roots are rational too.

Delta = 0 The quadratic has one repeated real root.

Delta < 0 The quadratic has no real roots. It has a pair of complex roots which are conjugates of one another.

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