### Home > A2C > Chapter 9 > Lesson 9.2.2 > Problem9-91

9-91.

Decide which of the following equations have real roots, and which have complex roots without completely solving them.

1. $y = x^{2} − 6$

Find the discriminant.

$b^{2} − 4ac = 0^{2} − 4\left(1\right)\left(−6\right) = 24$

This equation has real roots.

1. $y = x^{2} + 6$

$b^{2} − 4ac = 0^{2} − 4\left(1\right)\left(6\right) = −24$

This equation has complex roots.

1. $y = x^{2} − 2x + 10$

See part (b).

This equation has complex roots.

1. $y = x^{2} − 2x − 10$

See part (a).

1. $y = \left(x − 3\right)^{2} − 4$

Find the vertex.
Is it above or below the x-axis?

1. $y = \left(x − 3\right)^{2} + 4$

See part (e).