Question

To find the points of discontinuity, we need to solve the equation y=(x+5)/x^2+11x+30

Answer 1

The points of discontinuity for a function occur where the function is undefined. In this case, the function y=(x+5)/(x^2+11x+30) will be undefined when the denominator is equal to zero, as division by zero is undefined.

Therefore, we need to solve the equation x^2+11x+30=0 to find the points of discontinuity. Factoring the quadratic equation, we get:

(x+5)(x+6)=0

Setting each factor to zero, we get:

x+5=0 --> x=-5
x+6=0 --> x=-6

Therefore, the function will be undefined at x=-5 and x=-6, making these the points of discontinuity for the function y=(x+5)/(x^2+11x+30).