Question

# If the roots of the quadratic equation $$x^{2}-4x-\log_{3}a=0$$ are real, then the least value of $$a$$ is

A
81
B
181
C
164
D
9

Solution

## The correct option is B $$\dfrac{1}{81}$$Given roots are real$$\Rightarrow b^{2}-4ac\geq 0$$$$\Rightarrow 16+4(\log_{3}a)\geq 0$$$$log_{3}{a}\geq -4$$$$a\geq 3^{-4}$$Least value of $$a$$ is $$\dfrac{1}{3^{4}}=\dfrac{1}{81}$$ .Mathematics

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