Let \( f(x)=a x^{3}+b x^{2}+c x+1 \) have extrema at \( x=\alpha, \...

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Let \( f(x)=a x^{3}+b x^{2}+c x+1 \) have extrema at \( x=\alpha, \beta \) such that \( \alpha \beta0 \) and \( f(\alpha) . f(\beta)0 \). Then the equation \( f(x)=0 \) has
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(a) three equal real roots
(b) three distinct real roots
(c) one positive root if \( f(\alpha)0 \) and \( f(\beta)0 \)
(d) one negative root if \( f(\alpha)0 \) and \( f(\beta)0 \)
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