Question

Use the discriminant to find the number of real solutions of the following quadratic equation: 2x^2 + 4x + 2 = 0.
A. no real solutions
B. 1 real solution
C. 2 real solutions
D. 3 real solutions

Answer 1

Discriminant of
\[ax^2+bx+c=0\]If it is less than 0 there is no solution, is is greater than 0 there are two solutions, if it is zero there is only one solution. In this case it is
\[b^2-4ac\]So,\[4^2-4\cdot2\cdot2=16-16=0\]There is only one real solution.