Multiple choice

If the equation $z^4+a_1z^3+a_2z^2+a_3z+a_4=0$, where $a_1, a_2, a_4$ are real coefficients different from zero, has a purely imaginary root, then the expression $\dfrac{a_3}{(a_1a_2)}+\dfrac{a_1a_4}{a_2a_3}$ has the value equal to

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

Let the imaginary root be ki. Substituting into the equation and separating real and imaginary parts allows one to solve for the coefficients. The resulting relation between the coefficients satisfies the given expression, yielding a value of 1.

Keep practicing — related questions