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Let α and β be the roots of the quadratic equation x2 - (p - 2)x + p - 6 = 0. What is the minimum possible value of α+ β2?
  • a)
    0
  • b)
    3
  • c)
    4
  • d)
    7
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Let αand βbe the roots of the quadratic equation x2 - (p - ...
 α+ β2 = (α + β )2 - 2αβ
From given equation, α + β = p - 2 and αβ = p - 6
Substituting values in equation (i), we get,
α+ β2 = p2 + 4 - 4p - 2(p - 6)
             = p2 + 4 - 4p - 2p + 12
             = p2 - 6p + 9 + 7
              = (p - 3)2 + 7
Minimum value of α+ β2 will be obtained by putting (p - 3) = 0
Minimum value = 7
Hence, option 4.
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Most Upvoted Answer
Let αand βbe the roots of the quadratic equation x2 - (p - ...
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Let αand βbe the roots of the quadratic equation x2 - (p - 2)x + p - 6 = 0. What is the minimum possible value ofα2+β2?a)0b)3c)4d)7Correct answer is option 'D'. Can you explain this answer?
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