Question

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

Answer 1

Answer:

The x-intercept of the function are at $(\frac{1 + \sqrt{57}}{2}, 0)$ and $(\frac{1 - \sqrt{57}}{2}, 0)$.

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

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

⇒ $x = \frac{1 + \sqrt{57} }{2}$ and $x = \frac{1 - \sqrt{57} }{2}$  

Therefore, the x-intercept of the function are at $(\frac{1 + \sqrt{57}}{2}, 0)$ and $(\frac{1 - \sqrt{57}}{2}, 0)$. (Answer)