Question

Is the following statement true or false: If b^2-4ac<0 then there are two complex roots of the quadratic equation ax^2+bx+c=0

Answer 1

And please state why the statement is true or false.

Answer 2

Do you know the Quadratic Formula? Consider how the Quadratic Formula is affected when \(b^2 - 4ac\) is negative:
\[ x_1 = \frac{-b + \sqrt{\color{goldenrod}{b^2 - 4ac}}}{2a} \\
x_2 = \frac{-b - \sqrt{\color{goldenrod}{b^2 - 4ac}}}{2a} \\ \] If that part is negative, then won't you always get a negative under the square root?

Answer 3

Oh okay I was wondering how it fits in but now that you highlight it, it makes sense thank you!!! I understand

Answer 4

You're welcome. :)