Question

Find all the zeros of polynomial f(X) =x³ - 2x

Answer 1

x^3-2x= 0

X(x^2-2)=0

x^2-2=0

x^2=2

x=+_√2

X=√2 & X= -√2

Answer 2

${\huge {\underline {\bf {\blue {Answer}}}}}$

Given: x³=2x

To find: all the zeroes of the given equation

1. Taking all the terms on LHS:

• let, x^3 - 2x = 0

2. Taking x common from both the terms:

• x(x^2 - 2) = 0

3. now, either x can be zero, or x^2 -2 can be zero

• x^2 - 2 = 0

solving this equation, we get

• x^2=2

• $x = +\sqrt{2\\} or x = -\sqrt{2}$

x=0

so, there are 3 zeroes and the zeroes of the given equation are 0, ±√2

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