Question

3. How many solutions are there to the
equation 2x^2 - 3x +12=0? Tell how
you know.

Answer 1

If you're talking about solutions in general (real and imaginary solutions), there is 2, because the fundamental theorem of algebra says that the number of roots of any polynomial is the degree if it's highest power, which is 2.

If you're talking about only real solutions, there is 0. To show that, we can take the discriminant (b^2-4ac) part of the quadratic equation, and plug in the know values. We then get:

(-3)^2-4*2*12

=9-96

=-87

Remember, the discriminant will be taken the square root. Since this is negative, the answer will be imaginary. Therefore, there is no real solution.