Suppose f(x) is such a quadrant expression that it is positive for all

1.	Suppose f(x) is such a quadrant expression that it is positive for all real x. If g(x) = f(x) + f’(x) + f’’(x), then for any real x. Then for any real x. a. g(x) < 0 b. g(x) > 0 c. g(x) = 0 d. g(x) ≥ 0
Answer» Correct option b. g(x) > 0 Explanation: Let f(x) = ax² + bx + c, a > 0, b² < 4ac (∵ f(x) > 0) Now, g(x) = ax² + bx + c + 2ax + b + 2a = ax²+ (b + 2a)x + 2a + b + c Now, (b + 2a)² - 4a(2a + b + c) = b² + 4ab + 4a² - 8a² - 4ab - 4ac = b² - 4ac - 8a² < 0 ⇒ g(x) > 0

Suppose f(x) is such a quadrant expression that it is positive for all real x. If g(x) = f(x) + f’(x) + f’’(x), then for any real x. Then for any real x. a. g(x) < 0 b. g(x) > 0 c. g(x) = 0 d. g(x) ≥ 0

Answer»

Correct option b. g(x) > 0

Explanation:

Let f(x) = ax² + bx + c, a > 0, b² < 4ac

(∵ f(x) > 0)

Now, g(x) = ax² + bx + c + 2ax + b + 2a

= ax²+ (b + 2a)x + 2a + b + c

Now, (b + 2a)² - 4a(2a + b + c)

= b² + 4ab + 4a² - 8a² - 4ab - 4ac

= b² - 4ac - 8a² < 0 ⇒ g(x) > 0

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Suppose f(x) is such a quadrant expression that it is positive for all real x. If g(x) = f(x) + f’(x) + f’’(x), then for any real x. Then for any real x. a. g(x) &lt; 0 b. g(x) &gt; 0 c. g(x) = 0 d. g(x) ≥ 0

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Suppose f(x) is such a quadrant expression that it is positive for all real x. If g(x) = f(x) + f’(x) + f’’(x), then for any real x. Then for any real x. a. g(x) < 0 b. g(x) > 0 c. g(x) = 0 d. g(x) ≥ 0