Question

Find the square root of the following polynomial by division method: $x^4-4x^3+10x^2-12x+9$

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

Answer 1

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

We find the square root of the given polynomial $x^4-4x^3+10x^2-12x+9$ by following the steps shown below:

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

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

Step 3. Double the currently displayed quotient $\left(x^2\right)$ to $2x^2$. Then add a new term, $x$, to the quotient such that the result will remove the first term, $(-4x^3)$, in the current partial remainder.

Step 4. Repeat steps 2 and 3 until done.

The division is as follows:

Hence, the square root of $x^4-4x^3+10x^2-12x+9$ is $x^2-2x+3$.