Question

Find the vertical asymptotes.

Simplify fractions and leave in improper form.
3x2 + 17x + 10
y =
6x2 - 11x + 4
X =
Ž, x =
4
[?]

Answer 1

x1 = 4/3, x2 = 1/2

Value to fill in the question mark: 3

Explanation:

The vertical asymptotes occurs when the denominator of y are 0, so the value of y goes to infinity.

So, to find the asymptotes, we need to calculate:

`6x^(2) - 11x + 4 = 0`

Using Bhaskara's formula. we have:

`\Delta = (-11)^2 - 4*6*4 = 25`

`√(\Delta) = 5`

`x_1 = (11 + 5)/12 = 4/3`

`x_2 = (11 - 5)/12 = 1/2`

So the value we need to fill in the question mark is 3