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The equationx^3 – 6(x^2) +15x +3 =0 has1)only one positive root2)two positive and one negative roots3)no positive root4)none of thesePlease show how to determine the types of roots in these kind of questions..

Meghendra Agrawal , 6 Years ago
Grade
anser 1 Answers
Arun

Last Activity: 6 Years ago

 
Dear Meghendra
 
f(x) = x^3 – 6x^2 + 15 x + 3
 
f(0) = 3
f( – 1) =  – 1 – 6 – 15 + 3 =  – 19
 
Hence one root lies between 0 and  – 1
 
f’(x) = 3x^2 – 12 x + 15
 
its D is always negative hence f’(x) is always positive hence f (x) is increasing function
 
only one real root which is negative

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