Question Details

Let A be a real number. Then the roots of the equation x24xlog2A=are real and distinct if and only if

Options

A

A>116

B

A>18

C

A<116

D

A<18

Show Answer

Correct Answer :

Option A

A>116

Solution :

For a quadratic equation ax2+bx+c=0 to have real and distinct roots, its discriminant must be strictly greater than zero.

D=b24ac>0

For the given equation x24xlog2A=0, we have:

a=1, b=4, c=log2A

Thus, the discriminant is:

D=(4)24(1)(log2A)>0

16+4log2A>0

4log2A>16

log2A>4

Since the base of the logarithm (2) is greater than 1, we can write:

A>24

A>116

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