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A beautiful equation is an equation whose roots are distinct and difference between roots is at least 26. Find the number of positive integral values of p if x2 – p x + 12 = 0 is a beautiful equation.
  • a)
    26
  • b)
    27
  • c)
    53
  • d)
    None of these
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
A beautiful equation is an equation whose roots are distinct and diffe...
Let roots are α & β
Then and α + β  = p and α β = 12.
► (α - β)2 = (α + β)2 - 4 α β
► p2 - 4(12)
► p2 - 48
Given |α - β| ≥ 26
► (α - β)2 ≥ 676
► p2 - 48 ≥ 676
► p2 ≥ 724
► p ∈ (-∞ - √724) ∪ (√724, ∞)
So, there is infinity many positive integral values of P.
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Most Upvoted Answer
A beautiful equation is an equation whose roots are distinct and diffe...
Let roots are α & β
Then and α + β  = p and α β = 12.
► (α - β)2 = (α + β)2 - 4 α β
► p2 - 4(12)
► p2 - 48
Given |α - β| ≥ 26
► (α - β)2 ≥ 676
► p2 - 48 ≥ 676
► p2 ≥ 724
► p ∈ (-∞ - √724) ∪ (√724, ∞)
So, there is infinity many positive integral values of P.
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A beautiful equation is an equation whose roots are distinct and difference between roots is at least 26. Find the number of positive integral values of p if x2– p x + 12 = 0 is a beautiful equation.a)26b)27c)53d)None of theseCorrect answer is option 'D'. Can you explain this answer?
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