Question

Find the number of zeroes in f(x)=(x-2)³-x³

Answer 1

Answer:

2 zeroes

Step-by-step explanation:

expression is (x-2)^3-x^3

x^3-2^3-3(2x)(2-x)-x^3. [since

(a-b)^3=a^3-b^3-3(ab)(a+b)]

so,

x^3-x^3 gets cancelled

so,

-8-6x(2-x)

-8-12x+6x^2

therefore, f(x)=6x^2-12x-8

the highest degree of f(x) is 2

therefore, f(x) will have 2 zeroes