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Oct. 8, 2020, 11:14 p.m.
Let A be a real number. Then the roots of the equation x^2 - 4x - log2A = 0 are real and distinct if and only if

Let A be a real number. Then the roots of the equation x2 - 4x - log2A = 0 are real and distinct if and only if

  1. A < 1/16
  2. A > 1/8
  3. A > 1/16
  4. A < 1/8
quant
cat-2019
logarithm
equations
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Oct. 8, 2020, 11:16 p.m.

For roots of any Quadratic equation to be real and distinct, D > 0

So, for x2 − 4x - logA = 0,
D = (-4)2 - (4 x 1 x (- logA)) > 0

16 + 4 logA> 0
4 + logA> 0
logA> -4
A > 1/24
A > 1/16

Therefore option 3

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