Question

Find the values of $a$ and $b$ if the following polynomial is perfect square: $4x^4-12x^3+37x^2+ax+b$

• A. $a=-42,b=49$
• B. $a=42,b=49$
• C. $a=-42,b=-49$
• D. None of these

Answer 1

The correct option is A $a=-42,b=49$

Firstly, we find the square root of the given polynomial $4x^4-12x^3+37x^2+ax+b$ by following the steps shown below:

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

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

Step 3. Double the currently displayed quotient $\left(2x^2\right)$ to $4x^2$. Then add a new term, $x$, to the quotient such that the result will remove the first term, $(-12x^3)$, 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 $a=-42$ and $b=49$.