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Grade:
        
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..
one year ago

Answers : (1)

Arun
24510 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
one year ago
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