Verified Solution • 2025–26 Session moderate

QJEEM04Ma033b: JEE Main 2004 Mathematics - Class 11 JEEM04Ma033b Solution: If one root of the equation is 4, while the equation has equal…

If one root of the equation x2+px+12=0{x^2} + px + 12 = 0 is 4, while the equation x2+px+q=0{x^2} + px + q = 0 has equal roots,
then the value of ′q′'q' is

Multiple Choice Options

  • A 4
  • B 12
  • C 3
  • D 494{{49} \over 4}

Step-by-Step Verified Solution

44 is a root of x2+px+12=0{x^2} + px + 12 = 0

⇒16+4p+12=0\Rightarrow 16 + 4p + 12 = 0

⇒p=−7\Rightarrow p = - 7

Now, the equation x2+px+q=0{x^2} + px + q = 0

has equal roots.

∴\therefore p2−4q=0{p^2} - 4q = 0 ⇒q=p24=494\Rightarrow q = {{{p^2}} \over 4} = {{49} \over 4}

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