JEE quadratic part 2

Algebra Level 4

Consider the inequality 9 x − a ⋅ 3 x − a + 3 ≤ 0 9^x - a \cdot 3^x - a + 3 \leq 0 where a a is a real parameter independent to x x . If this inequality has at least one positive solution, then find the range of a a .

( − ∞ , − 2 ) (-\infty,-2) [ 3 , ∞ ) [3,\infty) ( 2 , ∞ ) (2,\infty) [ − 2 , ∞ ) [-2,\infty)

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Tanishq Varshney by Tanishq Varshney , 23, India

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1 solution

Bhavesh Ahuja
Feb 17, 2015

Let 3^x be y. Then the above expression would become (y^2) - ay -a +3≤0. This becomes a simple quadratic whose roots are 2,-6. Hence this quadratic Is positive in the intervals (2,∞) and (-∞,-6).

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