Let \( f(x)=a_{5} x^{5}+a_{4} x^{4}+a_{3} x^{3}+a_{2} x^{2}+a_{1} x \), where \( a_{i}^{\prime} ... VIDEO
Let \( f(x)=a_{5} x^{5}+a_{4} x^{4}+a_{3} x^{3}+a_{2} x^{2}+a_{1} x \), where \( a_{i}^{\prime} \) s are real and \( f(x)=0 \) has a positive root \( \alpha_{0} \). Then
(a) \( f^{\prime}(x)=0 \) has a root \( \alpha_{1} \) such that \( 0\alpha_{1}\alpha_{0} \)
(b) \( f^{\prime}(x)=0 \) ahs at least one real root
(c) \( f^{\prime \prime}(x)=0 \) has at least two real roots
(d) none of these
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