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

1 Answer
George C.
Jun 14, 2015

2x^2+5x+5 has discriminant Delta = -15

Since Delta < 0 the equation has no real solutions, only a pair of complex ones.

Explanation:

2x^2+5x+5 is of the form ax^2+bx+c

with a=2, b=5 and c=5

This has discriminant given by the formula:

Delta = b^2-4ac = 5^2-(4xx2xx5) = 25 - 40 = -15

Since Delta < 0 the equation has no real solutions, only complex ones.

The possible cases are:

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

Delta = 0 : The equation has one (repeated) real solution.

Delta < 0 : The equation has two distinct complex roots (which are complex conjugates of one another).

Related questions
See all questions in Solutions Using the Discriminant
Impact of this question
1420 views around the world
You can reuse this answer
Creative Commons License