Given the equation

$3x^3+2x^2+x+5=0$

Has $n$ real roots and the sum of all the real roots is $l$

Determine the value of

$n-[l]$

Where [...] is the GIF of ...

The answer is 3.

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I did the same way . Good work. Upvoted :D

Keshav Tiwari
- 6 years, 4 months ago

I like your solution. Congratulations.

Niranjan Khanderia
- 6 years, 4 months ago

Nice solution

Paola Ramírez
- 6 years, 4 months ago

Yuppp did the same way

Rajat Bisht
- 6 years, 4 months ago

@Parth Lohomi I am really confused why does your problems move to level 5 and so less people can solve them. Was this worth 300+ points? 😕

Pranjal Jain
- 6 years, 4 months ago

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Really can you solve all my level 5 problems!?? 😕

Parth Lohomi
- 6 years, 4 months ago

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Hey! Cmon! I am not saying your problems are bad or something like that! They are nice! But when I solved it, it was worth 300+ points! And I was really surprised! Usually I have to work hard to get 300+ points' problem correct. Still let it be! Its down to 250 now. Keep up the hard work. ☺☺

Pranjal Jain
- 6 years, 4 months ago

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@Pranjal Jain – Is my solution correct ? I doubt !

Nihar Mahajan
- 6 years, 4 months ago

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- If you are given a particular cubic equation, you must check if it has 3 roots or not. Maybe it has only 1 root. Though in general, a cubic can have maximum of 3 roots.

$\lfloor a\rfloor+\lfloor b\rfloor+\lfloor c\rfloor ≠\lfloor (a+b+c)\rfloor$ . A counterexample can be $1.2,1.5,2.9$

Pranjal Jain
- 6 years, 4 months ago

Obviously I can't solve all of your problems! 😅

Pranjal Jain
- 6 years, 4 months ago

I met your brother vatsal today! ! I even know your house!!!! I Live very close to you,, in gopal vihar @Pranjal Jain

Parth Lohomi
- 6 years, 4 months ago

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Oh I see! So many Brilliantians are from Kota!

Pranjal Jain
- 6 years, 4 months ago

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@Pranjal Jain – I think you are right @Pranjal Jain

Rajat Bisht
- 6 years, 4 months ago

You can not say that!😡😡😬😬😠!

Parth Lohomi
- 6 years, 4 months ago

6 Helpful
0 Interesting
0 Brilliant
0 Confused

This is the best one !!!!!!

Shubhendra Singh
- 6 years, 4 months ago

Please tell me how to plot this

Mehul Chaturvedi
- 6 years, 4 months ago

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I will put this in a note.

Chew-Seong Cheong
- 6 years, 4 months ago

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$f(x)=3x^3+2x^2+x+5$

$g(x)=f'(x)=9x^2+4x+1$

Now $g(x)$ is always positive as coefficient of $x^2>0$ and $∆<0$

Therefore, $f(x)$ is strictly increasing and hence $n=1$ .

Thus $f(x)=0$ has a solution between $x=-2$ and $x=-1$ .

$\Rightarrow \lfloor l\rfloor=-2$

$n-\lfloor l \rfloor=1+2=3$