Answer:
The x-intercept of the function are at [tex](\frac{1 + \sqrt{57}}{2}, 0)[/tex] and [tex](\frac{1 - \sqrt{57}}{2}, 0)[/tex].
Step-by-step 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, [tex]x = \frac{-(- 1) + \sqrt{(-1)^{2} - 4(1) (- 14) } }{2(1)}[/tex] and
[tex]x = \frac{-(- 1) - \sqrt{(-1)^{2} - 4(1) (- 14) } }{2(1)}[/tex]
⇒ [tex]x = \frac{1 + \sqrt{57} }{2}[/tex] and [tex]x = \frac{1 - \sqrt{57} }{2}[/tex]
Therefore, the x-intercept of the function are at [tex](\frac{1 + \sqrt{57}}{2}, 0)[/tex] and [tex](\frac{1 - \sqrt{57}}{2}, 0)[/tex]. (Answer)
