Flag Algebra> The equation x^3 – 6(x^2) +15x +3 =0 has ...
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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..

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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