Question

I'm having trouble finding the x-intercepts AND the y-intercept, could some help and explain there work?? :)))) thank you!!

f(x)= x^3 - 4x^2 - 11x + 30

Answer 1

Hello,

`f(x)=x^3-4x^2-11x+30 \\\\f(0)=30`

so y-intercept is (0,30)

The product of the roots are -30 = 2 * 5 * -3, and the sum is 4 = 2 + 5 - 3 , so we can factorise

`f(x)=x^3-4x^2-11x+30 \\\\f(x)=0 \\\\<=> x^3-4x^2-11x+30=(x+3)(x-2)(x-5)=0\\\\<=> x=-3 \ or \ x=2 \ or \ x=5`

x-intercepts are (-3,0) (2,0) and (5,0)

thanks