Question

For all x,x? + 2ax - 5a + 6 > 0, then the range of 'a' is

Answer 1

Given : for all x ∈ R, x² + 2ax - 5a + 6 > 0

To find : The range of a.

solution : we know, ax² + bx + c > 0 for all x ∈ R only if a > 0 , D < 0

given x² + 2ax - 5a + 6 > 0

here D = (2a)² - 4(-5a + 6) < 0

⇒4a² + 20a - 24 < 0

⇒a² + 5a - 6 < 0

⇒a² + 6a - a - 6 < 0

⇒a(a + 1) - 6(a + 1) < 0

⇒(a - 6)(a + 1) < 0

⇒-1 < a < 6

Therefore the range of a is (-1, 6).

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