Question

Number of integral roots of| X - 1 | |x^2 – 2 \= 2 is​

Answer 1

Answer:

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Answer 2

Concept

The numbers which satisfy the worth of a polynomial are called its roots .

Given

The given expression is $\left|x-1\right|\left|x^2-2\right|=2$.

Find

We have to search out the amount of integral roots of the given expression.

Solution

we will solve it by making the cases.

The first case is $\left|x-1\right|=1$.

When $x-1=1$ then $x=2$ and When $-\left(x-1\right)=1$ then $x=0$.

Thus, we are saying that $x\in\{0,2\}$.       ......(1)

The Second case is $\left|x^2-2\right|=2$.

When $x^2-2=2$ then $x=\pm 2$ and when $-\left(x^2-2\right)=2$ then $x=0$.

From the second case we are saying that $x\in \{-2,2\}$.     ......(2)

The third case is $\left|x-1\right|=2$ .

When $x-1=2$ then we cannot consider the worth of because the worth is in root $\pm 2$and when $-\left(x-1\right)=2$ then $x=-1$.

From this case we are saying that $x\in \{2\}$.       ......(3)

The fourth case is $\left|x^2-2\right|=1$.

when $x^2-2=1$ then we cannot consider the value of $x$ because the value is in root and when $-\left(x^2-2\right)=1$ then $x=\pm 1$.

From this case we say that $x\in \{-1,1\}$       ......(4)

Total integral solution from equation (1),(2),(3) and (4) is $x\in \{-1,0,2\}$.

Hence, the quantity of integral roots is $3.$

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