Multiple choice

The equation $x\left(\dfrac{3}{4}(log_2x)^2+log_2x-\dfrac{5}{4}\right)=\sqrt2$ has

  1. at least one real root

  2. exactly one irrational

  3. exactly two rational root

  4. exactly one rational root
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let u = log2(x). The equation is x(3/4*u^2 + u - 5/4) = sqrt(2). This is a transcendental equation. Testing values or analyzing the function shows it has one irrational root.

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