Question

What are the x-intercepts of f(x)=x2+3x+2−4x−16.

Answer 1

The x-intercept of the function are at
`((1 + √(57))/(2), 0)` and
`((1 - √(57))/(2), 0)`.

Explanation:

The given function is f(x) = x² + 3x + 2 - 4x - 16

Now, we have to find the x-intercept of this function.

So, at x-intercept y = f(x) = 0.

Then, x² + 3x + 2 - 4x - 16 = 0

⇒ x² - x - 14 = 0

The left hand side can not be factorized. So, apply Sridhar Acharya's formula.

Therefore,
`x = \frac{-(- 1) + \sqrt{(-1)^(2) - 4(1) (- 14) } }{2(1)}` and

`x = \frac{-(- 1) - \sqrt{(-1)^(2) - 4(1) (- 14) } }{2(1)}`

⇒
`x = (1 + √(57) )/(2)` and
`x = (1 - √(57) )/(2)`

Therefore, the x-intercept of the function are at
`((1 + √(57))/(2), 0)` and
`((1 - √(57))/(2), 0)`. (Answer)