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

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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

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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