Question

Find the square root of the following polynomial by division method: $9x^4-6x^3+7x^2-2x+1$

• A. $|3x^2-x+1|$
• B. $|3x^2-x-1|$
• C. $|3x^2+x+1|$
• D. None of these

Answer 1

The correct option is A $|3x^2-x+1|$

We find the square root of the given polynomial $9x^4-6x^3+7x^2-2x+1$ by following the steps shown below:

Step 1. Compute the square root of the leading term $\left(9x^4\right)$ and put it, $\left(3x^2\right)$, in the two places shown.

Step 2. Subtract and bring down the next two terms.

Step 3. Double the currently displayed quotient $\left(3x^2\right)$ to $6x^2$. Then add a new term, $x$, to the quotient such that the result will remove the first term, $(-6x^3)$, in the current partial remainder.

Step 4. Repeat steps 2 and 3 until done.

The division is as follows:

Hence, the square root of $9x^4-6x^3+7x^2-2x+1$ is $3x^2-x+1$.