If $ \alpha $ and $ \beta$ are the roots of the equation $ { ax }^{ 2 }+bx+c=0$ ($ a\neq 0,a.b,c$ being different), then $ \left( 1+\alpha +{ \alpha }^{ 2 } \right) \left( 1+\beta +{ \beta }^{ 2 } \right) $ is equal to
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Zero
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Positive
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Negative
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None of these
B
Correct answer
Explanation
The expression (1+alpha+alpha^2)(1+beta+beta^2) expands to 1 + (alpha+beta) + (alpha^2+beta^2) + alpha*beta + alpha^2*beta^2 + alpha*beta*(alpha+beta) + alpha^2*beta^2. Using Vieta's formulas (alpha+beta = -b/a, alpha*beta = c/a), this simplifies to a positive value for real roots of a quadratic.