If $a,b,c$ are real and ${x^3} - 3{b^2}x + 2{c^3}$ is divisible by $x - a$ and$x - b$, then

  • A

    $a = - b = - c$

  • B

    $a = 2b = 2c$

  • C

    $a = b = c$,$a = - 2b = - 2c$

  • D

    None of these

Similar Questions

If $x$ is a solution of the equation, $\sqrt {2x + 1}  - \sqrt {2x - 1}  = 1, \left( {x \ge \frac{1}{2}} \right)$ , then $\sqrt {4{x^2} - 1} $ is equal to 

  • [JEE MAIN 2016]

The product of all real roots of the equation ${x^2} - |x| - \,6 = 0$ is

The number of solutions for the equation ${x^2} - 5|x| + \,6 = 0$ is

Consider a three-digit number with the following properties:

$I$. If its digits in units place and tens place are interchanged, the number increases by $36$ ;

$II.$ If its digits in units place and hundreds place are interchanged, the number decreases by $198 .$

Now, suppose that the digits in tens place and hundreds place are interchanged. Then, the number

  • [KVPY 2017]

In the equation ${x^3} + 3Hx + G = 0$, if $G$ and $H$ are real and ${G^2} + 4{H^3} > 0,$ then the roots are