Question

Find the zeroes of the polynomial x3-4x2+4x

Answer 1

Step-by-step explanation:

done by ayush miglani.............

Answer 2

The zeroes of the polynomial are 0,2,2.

Step-by-step explanation:

The given polynomial is

$P(x)=x^3-4x^2+4x$

We need to find the zeroes of the polynomial.

$P(x)=x(x^2-4x+4)$

Splitting the middle term we get

$P(x)=x(x^2-2x-2x+4)$

$P(x)=x(x(x-2)-2(x-2))$

$P(x)=x(x-2)(x-2)$

$P(x)=x(x-2)^2$

Equate P(x)=0, to find the zeroes.

$x(x-2)^2=0$

Using zero product property we get

$x=0$

$(x-2)^2=0$

$x-2=0$

$x=2$ (With multiplicity 2)

Therefore, the zeroes of the polynomial are 0,2,2.

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