Question

What are the zeros of the function? f(x)=x3+x2−6x

Answer 1

x = - 3, x = 0, x = 2

Explanation:

To find the zeros equate f(x) to zero, that is

x³ + x² - 6x = 0 ← factor out x from each term

x(x² + x - 6) = 0

x(x + 3)(x - 2) = 0

Equate each factor to zero and solve for x

x = 0

x + 3 = 0 ⇒ x = - 3

x - 2 = 0 ⇒ x = 2

Answer 2

Answer: The zeroes of the given function are -3, 0 and 2.

Step-by-step explanation: We are given to find the zeroes of the following function :

`f(x)=x^3+x^2-6x~~~~~~~~~~~~~~~~~~~~(i)`

We know that

zeroes of a function y = f(x) are found by solving the following equation :

f(x) = 0.

Therefore, from equation (i), we have

`x^3+x^2-6x=0\\\\\Rightarrow x(x^2+x-6)=0\\\\\Rightarrow x(x^2+3x-2x-6)=0\\\\\Rightarrow x(x(x+3)-2(x+3))=0\\\\\Rightarrow x(x-2)(x+3)=0\\\\\Rightarrow x=0,~~x-2=0,~~x+3=0\\\\\Rightarrow x=0,~2,~-3.`

Thus, the zeroes of the given function are -3, 0 and 2.