CAT Question > How many integers “a” are there such that 9x...

How many integers “a” are there such that 9x^{2} + 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?

If 9x^{2} + 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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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.