Multiple choice

If $a,b,c$ are non-zero, unequal rational numbers, then the roots of the equation $\displaystyle abc^{2}x^{2}+(3a^{2}+b^{2})cx-6a^{2}-ab+2b^{2}=0$ are

  1. rational

  2. imaginary

  3. irrational

  4. none of these
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A Correct answer
Explanation

The discriminant D = [(3a^2+b^2)c]^2 - 4(abc^2)(-6a^2-ab+2b^2). Simplifying this expression shows it is a perfect square, implying the roots are rational.

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