+0

-2
44
2
+109

1.) Let$f(x) = \left\{ \begin{array}{cl} 2x + 1 & \text{if } x \le 3, \\ 8 - 4x & \text{if } x > 3. \end{array} \right.$Find the sum of all values of $x$ such that $f(x) = 0.$

2.) The graph of $y=\frac{5x^2-9}{3x^2+5x+2}$ has vertical asymptotes at $x = a$ and $x = b$. Find $a + b$.

Aug 23, 2020

#1
0

1. x = 14.

2. a + b = -1 + 8 = 7.

Aug 23, 2020
#2
+109
-1

Sorry, but you answer is wrong as you've used some random numbers. The correct answer is below:

The vertical asymptotes will occur when the denominator of a simplified rational expression is equal to zero. We factor the denominator $$3x^2+5x+2$$ to obtain $$(3x + 2)(x + 1)$$. Hence, there are vertical asymptotes when $$x=1,-2/3$$, and the sum of these values of $$-1-2/3$$ is $$-5/3$$

(We can also use Vieta's formulas, which states that the sum of the roots of $$ax^2+bx+c=0$$ is $$-b/a$$.)

Aug 24, 2020