Home
Class 12
MATHS
If f(x) is a non-zero polynomial of degr...

If f(x) is a non-zero polynomial of degree four, having loca extreme points at `x=-1,0,1` then the set `S={x in R:f(x)=f(0)}` contains exactly

A

`k` has one rational &` two irarational roots

B

`k` has four rational roots

C

`k` has four irrational roots

D

`k` has three irrational roots.

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • JEE MAINS

    JEE MAINS PREVIOUS YEAR|Exercise Physics|30 Videos

  • JEE MAIN 2024 ACTUAL PAPER

    JEE MAINS PREVIOUS YEAR|Exercise Question|598 Videos

  • JEE MAINS 2020

    JEE MAINS PREVIOUS YEAR|Exercise MATHEMATICS|250 Videos

Similar Questions

Explore conceptually related problems

If f(x) is a non-zero polynomial of degree four, having local extreme points at x=-1,0,1 then the set S={x in R:f(x)=f(0)} contains exactly (a) four rational numbers (b) two irrational and two rational numbers (c) four irrational numbers (d) two irrational and one rational number

Suppose f(x) is a polynomial of degree four , having critical points at - 1,0,1. If T = (x in R|f (x) = f(0)} , then the sum of sqaure of the elements of T is .

Let f(x) be an non - zero polynomial of degree 4. Extremum points of f(x) are 0,-1,1 . If f(k)=f(0) then,

Let f(x) be a polynomial of degree four having extreme values at x=1 and x=2. If lim_(x to 0)(1+(f(x))/(x^(2)))=3, then f(2) is equal to

Let f(x) be a polynomial of degree four having extreme values at x""=""1 and x""=""2 . If (lim)_(xvec0)[1+(f(x))/(x^2)]=3 , then f(2) is equal to : (1) -8 (2) -4 (3) 0 (4) 4

If f (x) is a polynomial of degree two and f(0) =4 f'(0) =3,f'' (0) 4 then f(-1) =

If f(x) is a polynomial of degree n such that f(0)=0,f(x)=(1)/(2),...,f(n)=(n)/(n+1) then the value of f(n+1) is

If f(x) is a polynomial of degree 5 with real coefficientssuch that f(|x|)=0 has 8 real roots,then the number of roots of f(x)=0

If f(x) is a polynomial of degree 5 with real coefficients such that f(|x|)=0 has 8 real roots, then f(x)=0 has

If f(x) is a polynomial of degree four with leading coefficient one satisfying f(1)=1,f(2)=2,f(3)=3. then [(f(-1)+f(5))/(f(0)+f(4))]

JEE MAINS PREVIOUS YEAR-JEE MAINS-Physics
  1. If f(x) is a non-zero polynomial of degree four, having loca extreme p...

    Text Solution

    |

  2. The moment of inertia of a solid sphere, about an axis parallel to its...

    Text Solution

    |

  3. A load of mass M kg is suspended from a steel wire of length 2 m and r...

    Text Solution

    |

  4. In the value circuit, C=(sqrt(3))/(2)muF,R2=20omega, L=sqrt(3)/(10)H, ...

    Text Solution

    |

  5. An ideal gas is enclosed in a cylinder at pressure of 2 atm and temper...

    Text Solution

    |

  6. In the figure, given that V(BB) supply can vary from 0 to 5.0V,V(CC)=5...

    Text Solution

    |

  7. In the circuit shown, find C if the effective capacitance of the whole...

    Text Solution

    |

  8. An alpha-particle of mass m suffers 1-dimentinal eleastic collision wi...

    Text Solution

    |

  9. A 10 m long horizontal wire extends from North east ro South East. It ...

    Text Solution

    |

  10. To double the covering range of a TV transmittion tower, its height sh...

    Text Solution

    |

  11. A plano-convex lens (focal length f2, refractive indexmu(2), radius of...

    Text Solution

    |

  12. A vertical closed cylinder is separated into two parts by a frictionle...

    Text Solution

    |

  13. Two satellites, A and B, have masses m and 2m respectively. A is in a ...

    Text Solution

    |

  14. A long cylinderical vessel is half filled with a liquid. When the vess...

    Text Solution

    |

  15. A block kept on a rough inclined plane ,as shown in the figure, remain...

    Text Solution

    |

  16. In a Frank-Hertz experiment,an electron of energy 5.6eV passes through...

    Text Solution

    |

  17. A particle of mass 20 g is released with an initial velocity 5m//s alo...

    Text Solution

    |

  18. A galavanometer, whose resistance is 50 ohm has 25 divisions in it. Wh...

    Text Solution

    |

  19. A soap bubble,blown by a mechanical pump at the mouth of a tube, incre...

    Text Solution

    |

  20. In the given circuit diagram, the currents, I1=-0.3A,I4=0.8A and I5=0....

    Text Solution

    |

  21. A resonance tube is old and has jagged end. It is still used in the la...

    Text Solution

    |