Multiple choice

The roots of the equation $2\sqrt {x} +2x +{\dfrac {1}{2}}=0$ can be found by solving ______.

  1. $4x^2-25 x+4 =0 $
  2. $4x^2 - 25 -4 =0$
  3. $4x^2-17 x+4 =0$

  4. None of these
Reveal answer Fill a bubble to check yourself
D Correct answer
AI explanation

Let sqrt(x) = y. The equation becomes 2y + 2y^2 + 1/2 = 0, which simplifies to 4y^2 + 4y + 1 = 0. This factors into (2y + 1)^2 = 0, giving y = -1/2. Since y is the square root of x, it cannot be negative, meaning the original equation has no real roots. Substituting y = -1/2 into any quadratic form like 4x^2 - 25x + 4 = 0 is invalid, making None of these the only correct choice.

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