Multiple choice

The number of imaginary roots of the equation $4x(x^2+x+3)+5x(x^2-5x+3)=-\dfrac 32$ is

  1. $4$
  2. $0$
  3. $1$
  4. $2$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Expanding the equation: 4x^3 + 4x^2 + 12x + 5x^3 - 25x^2 + 15x = -1.5, which simplifies to 9x^3 - 21x^2 + 27x + 1.5 = 0. Dividing by 1.5 gives 6x^3 - 14x^2 + 18x + 1 = 0. By analyzing the derivative, the function is strictly increasing, meaning it has only one real root, hence two imaginary roots.

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