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How many integers “a” are there such that 9x2 + 3ax + (a + 5) > 0 for all values of x ?
  • a)
    7
  • b)
    8
  • c)
    9
  • d)
    10
Correct answer is option 'C'. Can you explain this answer?

Answers

If 9x2 + 3ax + (a + 5) > 0 for all values of x, then the discriminant of this quadratic expression must be negative.
⇒ (3a)2 -4(9) (a + 5) < 0="" or="" />2 - 4a - 20 < 0="" or="" r="" (a="" -="" />2 < />
⇒ -2.89
⇒ a = -2, -1,0, 1, 2, 3, 4, 5, 6
⇒ there are 9 such integral values.
Hence (c) is the correct option.

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How many integers “a” are there such that 9x2 + 3ax + (a + 5) > 0 for all values of x ?a)7b)8c)9d)10Correct answer is option 'C'. 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 How many integers “a” are there such that 9x2 + 3ax + (a + 5) > 0 for all values of x ?a)7b)8c)9d)10Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for CAT 2023 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for How many integers “a” are there such that 9x2 + 3ax + (a + 5) > 0 for all values of x ?a)7b)8c)9d)10Correct answer is option 'C'. Can you explain this answer?.
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If 9x2 + 3ax + (a + 5) > 0 for all values of x, then the discriminant of this quadratic expression must be negative.⇒ (3a)2 -4(9) (a + 5) 2 - 4a - 20 2 ⇒ -2.89⇒ a = -2, -1,0, 1, 2, 3, 4, 5, 6⇒ there are 9 such integral values.Hence (c) is the correct option.