Question

If $f\left(x\right)=\prod_{k = 1}^{999} \left(x^{2} - 47 x + k\right)$ , then product of all real roots of $f\left(x\right)=0$ is

• A. $550!$
• B. $551!$
• C. $552!$
• D. $999!$

Answer 1

Answer: (C)

Consider $x^{2}-47x+k=0$
For real roots, $47^{2}-4k\geq 0\Rightarrow k\leq 552$
$\therefore \, \, \, k=1, 2, 3\ldots .,552$
Product of real roots $=1\times 2\times 3\times 4\times \ldots ..\times 552=552!$