For which Value of m does the Graph of y = 18x2 + mx + 2 have Exactly One X-Intercept?
We will be using the concept of discriminant to solve this.
Answer: The Graph of y = 18x2 + mx + 2 will have exactly one x-intercept if m = ±12.
Let's solve this step by step.
Given that, y = 18x2 + mx + 2
18x2 + mx + 2 = 0
Discriminant = m2 - 4 × 18 × 2 = m2 - 144
We will have exactly one x-intercept if the discriminant is equal to zero.
⇒ m2 - 144 = 0
m2 = 144
m = ±12
That is, for y = 18x2 − 12x + 2 and y = 18x2 + 12x + 2