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The equation 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..

2 years ago

Answers : (1)

Arun
24738 Points
							
 
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
2 years ago
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