How do you find all zeros of the function $f(x)=(x+5)^3(x-4)(x+1)^2$ ?

Question

3346 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-07-06T14:34:55

$color(blue)(x=-5,x=-5,x=-5 , x=4, x=-1$

We first equate $(x+5)^3(x-4)(x+1)$ to zero:

$(x+5)(x+5)(x+5)(x-4)(x+1)=0$

We just find values of x that make each bracket in turn zero.

Solutions here are:

$x=-5,x=-5,x=-5 , x=4, x=-1$

The graph confirms this:

enter image source here

How do you find all zeros of the function f(x)=(x+5)^3(x-4)(x+1)^2f(x)=(x+5)^3(x-4)(x+1)^2?