Question

Find the values of $a$ and $b$ if the following polynomial is perfect square: $a{x}^4-b{x}^3+40x^2+24x+36$

• A. $a=9,b=-12$
• B. $a=9,b=12$
• C. $a=-9,b=-12$
• D. None of these

Answer 1

The correct option is A $a=9,b=-12$

Firstly, we find the square root of the given polynomial $a{x}^4-b{x}^3+40x^2+24x+36$ or $36+24x+40x^2-b{x}^3+a{x}^4$ by following the steps shown below:

Step 1. Compute the square root of the leading term $36$ and put it, $6$, in the two places shown.

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

Step 3. Double the currently displayed quotient $6$ to $12$. Then add a new term, $x$, to the quotient such that the result will remove the first term, $\left(24x\right)$, in the current partial remainder.

Step 4. Repeat steps 2 and 3 until done.

The division is as follows:

Hence, from the above division, we conclude that $a=9$ and $b=-12$.