Multiple choice

Let a, b, c be real numbers with a ≠ 0 and let α, ß be the roots of the equation ax2 + bx + c = 0. Then, the roots of the equation a3x2 + abcx + c3 = 0, in terms of α, ß, are given by

  1. α, ß

  2. cα/a, cß/a

  3. aα, cß

  4. cα, aß

  5. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

If ax^2 + bx + c = 0 has roots alpha, beta, then alpha+beta = -b/a and alpha*beta = c/a. For a^3x^2 + abcx + c^3 = 0, divide by a^3: x^2 + (bc/a^2)x + (c^3/a^3) = 0. The roots are (c/a)alpha and (c/a)beta.

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