Question

The number of integral values of $b$, which the equation $x^2+bx-16=0$ has integral roots, is

• A. $2$
• B. $3$
• C. $4$
• D. $5$
• E. $6$

Answer 1

The correct option is A

$2$

Explanation for the correct option:

Find the number of integral values of $b$.

An equation $x^2+bx-16=0$ is given.

Find the roots of the given equation as follows:

$$\begin{gathered} x=\frac{-b\pm \sqrt{b^2-4(-16)}}{2} \\ \Rightarrow x=\frac{-b\pm \sqrt{b^2+64}}{2} \end{gathered}$$

Since, $x$ is an integer, which is possible only when $-b\pm \sqrt{b^2+64}$ is even.

We know that, only the sum and subtraction of the even numbers is an even number.

Which implies that, $b$ and $\sqrt{b^2+64}$ are even number.

Also, $b$ is an integer.

Therefore, the values of $b$ which satisfy all the conditions is $b=\pm 6$.

Thus, the number of integral values of $b$ is $2$.

Hence, option $A$ is the correct answer.