Question

If $x^2-bx+c=0$ has equal integral roots, then

• A. $b$ and $c$ are integers.
• B. $b$ and $c$ are even integers.
• C. $b$ is an even integer and $c$ is a perfect square of an integer.
• D. none of these.

Answer 1

Answer: (A), (C)

$b$ is an even integer and $c$ is a perfect square of an integer.
$b$ and $c$ are integers.

Given equation $x^2-bx+c=0$

Let $\alpha ,\alpha$ be equal integral roots.

So, $\alpha +\alpha =b,\alpha .\alpha =c$

$\therefore b=2\alpha ,c={\alpha }^2$.

Since, $\alpha$ is integer, so $b$ is an even integer.

Also, $c$ is perfect square of an integer.