Question

the roots of the equation X cube minus 2 x square minus x + 2 is equal to zero are​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

The zeros of the equation are: $x=2,\:x=-1,\:x=1$.

Step-by-step explanation:

Consider the provided equation.

$x^3-2x^2-x+2=0$

The above equation can be written as:

$(x^3-2x^2)-(x-2)=0$

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

Factor out x-2.

$(x-2)(x^2-1)=0$

$(x-2)(x^2-1^2)=0$

Use the formula: $a^2-b^2=(a-b)(a+b)$

$(x-2)(x-1)(x+1)=0$

Now by zero product rule: $\text{If}\:ab=0\:\mathrm{then}\:a=0\:\mathrm{or}\:b=0$

$(x-2)=0\ or\ (x-1)=0\ or\ (x+1)=0$

$x=2\ or\ x=1\ or\ x=-1$

Therefore, the zeros of the equation are: $x=2,\:x=-1,\:x=1$.

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