Multiple choice

a, b, c, are real numbers in the polynomial , $p\left( z \right) = 2{z^4} + a{z^3} + b{z^2} + cz + 3.$ If two roots of the equation $p\left( z \right) = 0$ are 2 and i. Then which of the following are false .

  1. $a = - {{11} \over 2}$

  2. b=5
  3. c = $ - {{11} \over 2}$

  4. a=-11
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Since coefficients are real, if i is a root, -i is also a root. Roots are 2, i, -i, r. Product of roots = 3/2 = 2 * i * (-i) * r = 2 * 1 * r = 2r. So r = 3/4. Sum of roots = -a/2 = 2 + i - i + 3/4 = 11/4. a = -11/2. Option D claims a = -11, which is false.

Keep practicing — related questions