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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..
The equation  x^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..

```
2 years ago

Arun
25768 Points
```							 Dear Meghendra f(x) = x^3 – 6x^2 + 15 x + 3 f(0) = 3f( – 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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