CPM Homework Help : A2C Problem 9-91

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Home > A2C > Chapter 9 > Lesson 9.2.2 > Problem 9-91

9-91.

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

$y = x^{2} − 6$
Hint (a):
Find the discriminant.
$b^{2} − 4ac = 0^{2} − 4\left(1\right)\left(−6\right) = 24$
Answer (a):
This equation has real roots.

$y = x^{2} + 6$
Hint (b):
$b^{2} − 4ac = 0^{2} − 4\left(1\right)\left(6\right) = −24$
Answer (b):
This equation has complex roots.

$y = x^{2} − 2x + 10$
Hint (c):
See part (b).
Answer (c):
This equation has complex roots.

$y = x^{2} − 2x − 10$
Hint (d):
See part (a).

$y = \left(x − 3\right)^{2} − 4$
Hint (e):
Find the vertex.
Is it above or below the x-axis?

$y = \left(x − 3\right)^{2} + 4$
Hint (f):
See part (e).

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