Multiple choice

The value of $p > 0$, for which both the equations $x^2 + px + 64 = 0$ & $x^2 - 8x + p = 0$ have equal roots is

  1. $8$
  2. $16$
  3. $32$
  4. $64$
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B Correct answer
Explanation

For equal roots, discriminant D = 0. Eq 1: p^2 - 4(64) = 0 => p^2 = 256 => p = 16 (since p>0). Eq 2: (-8)^2 - 4(p) = 0 => 64 = 4p => p = 16. Both equations yield p=16.

AI explanation

For a quadratic equation to have equal roots, its discriminant must equal zero. For the first equation x squared plus px plus sixty four equals zero, the discriminant condition is p squared equals two hundred fifty six, giving p equals sixteen. For the second equation x squared minus eight x plus p equals zero, the condition is sixty four minus four p equals zero, which also gives p equals sixteen.

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