How do you use the discriminant to find the number of real solutions of the following quadratic equation: 2x^2 + 4x + 2 = 0?

1 Answer
Alan P.
Jun 27, 2015

b^2-4ac = 4^2 - 4(2)(2) = 0 so this equation has exactly one real solution.

Explanation:

For a quadratic of the form ax^2+bx+c = 0
the solution roots are given by the quadratic formula: x=(-b+-sqrt(b^2-4ac))/(2a)

The discriminant is the portion (b^2-4ac)
if it is negative then the roots include a term which is the square root of a negative number; since there are no Real numbers whose square root is negative, when the discriminant is <0 there are no Real roots.

If the discriminant is =0 then +-sqrt(0) is a single value (+0 = -0)
and the quadratic has exactly one Real solution.

If the discriminant is >0 then +-sqrt("discriminant") represents two different values and the quadratic has two Real solutions.

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