» Q. If the root of the quadratic equation x^2-4x-log a(base3)=0 are real, then find the least value of a.

Options

1) 1/16

2) 1/8

3) 1/2

4) 1/9

5) 1/36

6) 1/27

7) 1/64

8) 1/72

9) 1/81

10)None of these

Answer

9

Explanation

Since the root of the given equation are real

Discriminant >= 0

16 + 4 log a(base3)>=0

log a(base3)>= -4

a >= 3^-4

a >= 1/81

option 9

or

For real root (-4)^2 - -4*1*(-log a(base3))>=0

or, 16+log a(base3)>=0

16>=-log a(base3)...(1)

so here least value of a according to the option 1/81 which satisfied (1)

so option is 9