Find all vertical asymptote of the rational function Enter y

Find all vertical asymptote of the rational function. (Enter your answers as a comma-separated list.) F(x) = 5x^2 - 3/4x^3 - 27x^2 + 35 x Find the zeros of the polynomial function. (Enter your answers as a comma-separated list. Enter all answers including repetitions.) P(x) = x^2 (3x + 4)^2

Solution

F(x) = (5x^2 -3)/( 4x^3 - 27x^2 +35x)

Vertical asymtotes : Vertical asymptotes are vertical lines which correspond to the zeroes of the denominator of arational function.

5x^2 -3 =0

x ^2 = 3/5

x = +/- sqrt(3/5)

x = sqrt(3/5)

x = -sqrt(3/5)

P(x) = x^2(3x +4)^2

zeros : x^2(3x +4)^2 =0

x = 0 ,0 ; 3x+4 = 0

x = -4/3

So, x = 0,0, -4/3 ,-4/3