Multiple choice

If one root of the equation $a{ x }^{ 2 } + bx + c = 0$ be the square of the other, then the value of ${ b }^{ 3 } + { a }^{ 2 }c + a{ c }^{ 2 } $ is

  1. $3abc$
  2. $abc$
  3. $6abc$
  4. $\dfrac{abc}{3}$
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A Correct answer
Explanation

If roots are alpha and alpha^2, then alpha + alpha^2 = -b/a and alpha^3 = c/a. Substituting alpha = (c/a)^(1/3) into the sum equation leads to the identity b^3 + a^2*c + a*c^2 = 3abc.

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