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The equaiton x^3 – 6(x^2) +15x +3 =0 has 1)only one positive root 2)two positive and one negative roots 3)no positive root 4)none of these Please show how to determine the types of roots in these kind of questions..

The equaiton  x^3 – 6(x^2) +15x +3 =0 has
1)only one positive root
2)two positive and one negative roots
3)no positive root
4)none of these
Please show how to determine the types of roots in these kind of questions..

Grade:

1 Answers

Arun
25763 Points
2 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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