The Discriminant

Question

2x2-7x-9=0 How many times will the graph of this equation cross the x-axis

Answer 1

The discriminate is b² - 4ac

Recall that ax² + bx + c = 0

So in your problem:

a = 2

b = -7

c = -9

So we just need to plug them in.

b² - 4ac

(-7)² - 4(2)(-9)

49 - 4(-18)

49 + 72

= 121 This is our discriminate

IF the discriminate is:

1. Positive - two real solutions
2. Zero - repeated real solutions
3. Negative - no real solutions

Since ours is positive 121, then we know there are two real solutions and therefore it crosses the x axis twice.