Register

TIFR-2011-Maths-A-11

413 views

1 Answer

1 votes
1 votes

Let F(x) = x3 + x + c

 F'(x)= 3x2 + 1

Since F' is always positive so F(x) is increasing everywhere.And since F(x) goes from minus infinity to plus infinity so it must be cutting x-axis at some point and that cutting point is the only root.

User Avatar
Voting & Accepting an answer helps improve the community
← PreviousNext →
← Previous in categoryNext in category →

Related questions

1 votes
1 votes
2 answers
1
makhdoom ghaya asked Dec 9, 2015
712 views
TIFR-2011-Maths-A-16
The polynomial $x^{4}+7x^{3}-13x^{2}+11x$ has exactly one real root.
The polynomial $x^{4}+7x^{3}-13x^{2}+11x$ has exactly one real root.
User Avatar
1 votes
1 votes
1 answer
2
makhdoom ghaya asked Dec 9, 2015
1,325 views
TIFR-2011-Maths-A-8
The sum of the squares of the roots of the cubic equation $x^{3}-4x^{2}+6x+1$ is 0. 4. 16. none of the above
The sum of the squares of the roots of the cubic equation $x^{3}-4x^{2}+6x+1$ is0. 4.16. none of the above
User Avatar
1 votes
1 votes
1 answer
3
makhdoom ghaya asked Dec 10, 2015
536 views
TIFR-2011-Maths-B-9
Let $P$ be a degree $3$ polynomial with complex coefficients such that the constant term is $2010$. Then $P$ has a root $\alpha$ with $|\alpha| > 10$.
Let $P$ be a degree $3$ polynomial with complex coefficients such that the constant term is $2010$. Then $P$ has a root $\alpha$ with $|\alpha| 10$.
User Avatar
1 votes
1 votes
0 answers
4
makhdoom ghaya asked Dec 9, 2015
323 views
TIFR-2011-Maths-A-24
The series $\sum_{n=1}^{\infty}\frac{\sqrt{n+1}-\sqrt{n}}{n}$ diverges.
The series$\sum_{n=1}^{\infty}\frac{\sqrt{n+1}-\sqrt{n}}{n}$diverges.
User Avatar
Link Copied!