Let $p(x)=x^2-5 x+a$ and $q(x)=x^2-3 x+b$, where $a$ and $b$ are positive integers. Suppose HCF $(p(x), q(x))=x-1$ and $k(x)=1 cm (p(x), q(x))$ If the coefficient of the highest degree term of $k(x)$ is 1 , then sum of the roots of $(x-1)+k(x)$ is

  • [KVPY 2014]
  • A

    $4$

  • B

    $5$

  • C

    $6$

  • D

    $7$

Similar Questions

The number of real solutions of the equation $|{x^2} + 4x + 3| + 2x + 5 = 0 $are

  • [IIT 1988]

Consider the quadratic equation $n x^2+7 \sqrt{n x+n}=0$ where $n$ is a positive integer. Which of the following statements are necessarily correct?

$I$. For any $n$, the roots are distinct.

$II$. There are infinitely many values of $n$ for which both roots are real.

$III$. The product of the roots is necessarily an integer.

  • [KVPY 2016]

The sum of the solutions of the equation $\left| {\sqrt x  - 2} \right| + \sqrt x \left( {\sqrt x  - 4} \right) + 2 = 0\left( {x > 0} \right)$ is equal to

  • [JEE MAIN 2019]

The maximum possible number of real roots of equation ${x^5} - 6{x^2} - 4x + 5 = 0$ is

A man standing on a railway platform noticed that a train took $21\, s$ to cross the platform (this means the time elapsed from the moment the engine enters the platform till the last compartment leaves the platform) which is $88\,m$ long, and that it took $9 s$ to pass him. Assuming that the train was moving with uniform speed, what is the length of the train in meters?

  • [KVPY 2015]