Question

(3x^2+25x+8)/(x^2+7x-8)find the x intercept (s) or explain why there is none

Answer 1

Answer:

(-1/3, 0)

Explanation:

To find the x-intercepts, we need to make the function equals to zero and solve for x, so:

$\frac{3x^2+25x+8}{x^2+7x-8}=0$

Now, we need to factorize the numerator and the denominator as follows:

$\frac{3x^2+25x+8}{x^2+7x-8}=\frac{(3x+1)(x+8)}{(x-1)(x+8)}=0$

So, we can simplify the expression as:

$\frac{3x+1}{x-1}=0$

Finally, a division is equal to zero only if the numerator is equal to zero. So:

$\begin{gathered} 3x+1=0 \\ 3x+1-1=0-1 \\ 3x=-1 \\ \frac{3x}{3}=-\frac{1}{3} \\ x=-\frac{1}{3} \end{gathered}$

Therefore, the x-intercept of the function is the point (-1/3, 0)