Question

What is the discontinuity and zero of the function f(x)= 2x2+5x-12/x+4

Answer 1

the answer is the 1st option
good luck :)

Answer 2

Option A.

Explanation:

The given function is f(x) =
`(2x^(2)+5x-12)/(x+4)`

If denominator of the fraction is zero then the function will be discontinued.

In other words at (x + 4) = 0 the given function will be discontinued.

x = -4 will be the point of discontinuity

Now we will find the factors of numerator to find the zeros of the function.

2x² + 5x - 12 = 2x² + 8x - 3x - 12

= 2x(x + 4) - 3(x + 4)

= (x + 4)(2x - 3)

Now these factors (x + 4) = 0 and (2x -3) are the zero factors of the function.

Therefore, x =
`(3)/(2)` will be the zero of the function.

In option A x = -4 is the point of discontinuity and (
`(3)/(2)`, 0) is the zero of the function.

Option A will be the correct option.