Multiple choice general knowledge math & puzzles

The equation 2x2 + 2(p + 1)x + p = 0, where p is real, always has roots that are

  1. Equal

  2. Equal in magnitude but opposite in sign

  3. Irrational

  4. Real
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For the quadratic equation 2x^2 + 2(p+1)x + p = 0, the discriminant is D = 4(p+1)^2 - 8p = 4(p^2+2p+1-2p) = 4(p^2+1). Since p^2+1 is always positive for all real p, D > 0 always. Therefore, the roots are always real and distinct.

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