Question

Find the square root of the following polynomial by division method: $4+25x^2-12x-24x^3+16x^4$

• A. $|4x^2-3x+2|$
• B. $|4x^2+3x+2|$
• C. $|4x^2-3x-2|$
• D. None of these

Answer 1

Answer: (A)

$|4x^2-3x+2|$

We find the square root of the given polynomial $16x^4-24x^3+25x^2-12x+4$ by following the steps shown below:

Step 1. Compute the square root of the leading term $\left(16x^4\right)$ and put it, $\left(4x^2\right)$, in the two places shown.

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

Step 3. Double the currently displayed quotient $\left(4x^2\right)$ to $8x^2$. Then add a new term, $x$, to the quotient such that the result will remove the first term, $(-24x^3)$, in the current partial remainder.

Step 4. Repeat steps 2 and 3 until done.

The division is as follows:

Hence, the square root of $16x^4-24x^3+25x^2-12x+4$ is $4x^2-3x+2$.