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Find all the values of p, such that 6 lies some where between the roots of the equation
x2 + 2(p - 3)x + 9 = 0. (‘x’ is a real number).
  • a)
    p < />
  • b)
    P > 6
  • c)
    0 < p="" />< />
  • d)
    0 < p="" />< />
Correct answer is option 'A'. Can you explain this answer?

Answers

Both the roots will be real as 6 lies between the roots
(i) b2 − 4ac > 0
= 4(p − 3)2 − 4 × 9 > 0P(P − 6) > 0
p > 6 or p < />
(ii), since x = 6 lies between the two roots.
so, (6)2 + 2(p − 3)6 + 9 < />
Hence the correct option is A.

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Find all the values of p, such that 6 lies some where between the roots of the equationx2 + 2(p - 3)x + 9 = 0. (‘x’ is a real number).a)p b)P > 6c)0 d)0 Correct answer is option 'A'. Can you explain this answer? for CAT 2023 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Find all the values of p, such that 6 lies some where between the roots of the equationx2 + 2(p - 3)x + 9 = 0. (‘x’ is a real number).a)p b)P > 6c)0 d)0 Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for CAT 2023 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find all the values of p, such that 6 lies some where between the roots of the equationx2 + 2(p - 3)x + 9 = 0. (‘x’ is a real number).a)p b)P > 6c)0 d)0 Correct answer is option 'A'. Can you explain this answer?.
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Both the roots will be real as 6 lies between the roots(i) b2 − 4ac > 0= 4(p − 3)2 − 4 × 9 > 0P(P − 6) > 0p > 6 or p (ii), since x = 6 lies between the two roots.so, (6)2 + 2(p − 3)6 + 9 Hence the correct option is A.