Question

The x intercepts of the function f(x) = 2x(x-5)^2(x+4)^3
are…

Answer 1

`\boxed{\sf x- intercepts = 0 , 5 \ and \ -4}`

Explanation:

A function is given to us and we need to find the x Intercepts of the graph of the given function . The function is ,

`\sf \implies f(x) = 2x( x - 5 ) ^2(x+4)^3`

For finding the x intercept , equate the given function with 0, we have ;

`\sf \implies 2x ( x - 5 )^2(x+4)^3= 0`

Equate each factor with 0 ,

`\sf \implies 2x = 0`

Divide both sides by 2 ,

`\sf \implies\bf x = 0`

Again ,

`\sf \implies ( x - 5)^2=0`

Taking squareroot on both sides,

`\sf \implies x - 5 = 0`

Add 5 to both sides,

`\sf \implies \bf x = 5`

Similarly ,

`\sf \implies \bf x = -4`

Hence the x Intercepts are -4 , 0 and 5 .

{ See attachment also for graph } .