# For which value of m does the graph of y = 18x^{2} + mx + 2 have exactly one x-intercept?

0, 9, 12, 16

**Solution: **

Given: Equation of graph y = 18x^{2} + mx + 2

Also it is given that the graph has only one intercept

We know that the graph will have two intercepts but if the determinant is 0 then the intercept will coincide.

The discriminant will be b^{2} - 4ac.

⇒ m^{2} - 4(18)(2)

⇒ m^{2} - 144

For intercept to coincide the determinant should be 0.

⇒ m^{2} - 144 = 0

⇒ m^{2} = 144

Applying square root on both sides

⇒ √m^{2} = √144

⇒ m = ±12

## For which value of m does the graph of y = 18x^{2} + mx + 2 have exactly one x-intercept?

**Summary: **

The graph y = 18x^{2} + mx + 2 will have only one intercept when m = 12 or m = -12.

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