Home
Class 12
MATHS
Consider the polynomial f(x) = 1+2x+3x...

Consider the polynomial
`f(x) = 1+2x+3x^(2)+4x^(3)`
Let s be the sum of all distinct real roots of `f(x)` end let `t = |s|`
The real number s lies in the interval.

A

`(3/4,3)`

B

`(21/64,11/16)`

C

`(9,10)`

D

`(0,(21)/(64))`

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRATION & ITS APPLICATION

    RESONANCE ENGLISH|Exercise Exercise 3 Part - II|25 Videos

  • DEFINITE INTEGRATION & ITS APPLICATION

    RESONANCE ENGLISH|Exercise High Level Problem|26 Videos

  • DEFINITE INTEGRATION & ITS APPLICATION

    RESONANCE ENGLISH|Exercise Exercise 2 Part - IV|6 Videos

  • COMBINATORICS

    RESONANCE ENGLISH|Exercise Exercise-2 (Part-II: Previously Asked Question of RMO)|5 Videos

  • DPP

    RESONANCE ENGLISH|Exercise QUESTION|656 Videos

Similar Questions

Explore conceptually related problems

Consider the polynomial f (x)= 1+2x+3x^2+4x^3 . Let s be the sum of all distinct real roots of f(x) and let t= |s| . The real number s lies in the interval. (a) (- 1/4, 0) (b) (- 11, - 3/4) (c) (- 3/4, - 1/2) (d) (0, 1/4)

Consider the polynomial f (x)= 1+2x+3x^2+4x^3 . Let s be the sum of all distinct real roots of f(x) and let t= |s| .

Consider the polynomial f (x)= 1+2x+3x^2+4x^3 . Let s be the sum of all distinct real roots of f(x) and let t= |s| .

Consider the polynomial f (x)= 1+2x+3x^2+4x^3 . Let s be the sum of all distinct real roots of f(x) and let t= |s| .

Consider the polynomial f (x)= 1+2x+3x^2+4x^3 . Let s be the sum of all distinct real roots of f(x) and let t= |s| .

Consider the polynomial f(x)=1 + 2x + 3x^2 +4x^3 for all x in R So f(x) has exactly one real root in the interval

The number of distinct real roots of x^4 - 4 x^3 + 12 x^2 + x - 1 = 0 is :

The sum of all the real roots of equation x^4-3x^3-2x^2-3x+1=0 is

If 4x^(2) + kx + 3 ge 0 for all real values of x then k lies in the interval

Let f(x) be a cubic polynomial defined by f(x)=x^(3)/(3)+(a-3)x^(2)+x-13. Then the sum of all possible values(s) of a for which f(x) has negative point of local minimum in the interval [ 1,5] is

RESONANCE ENGLISH-DEFINITE INTEGRATION & ITS APPLICATION -Exercise 3 Part - I
  1. Let f be a real-valued function defined on the inverval (-1,1) such th...

    Text Solution

    |

  2. Consider the polynomial f(x)= 1+2x+3x^2+4x^3. Let s be the sum of all ...

    Text Solution

    |

  3. Consider the polynomial f(x) = 1+2x+3x^(2)+4x^(3) Let s be the sum...

    Text Solution

    |

  4. Consider the polynomial f(x)= 1+2x+3x^2+4x^3. Let s be the sum of all ...

    Text Solution

    |

  5. T h ev a l u eofint(sqrt(1n2))^(sqrt(1n3))(xsinx^2)/(sinx^2+sin(1n6-x^...

    Text Solution

    |

  6. Let the straight line x= b divide the area enclosed by y=(1-x)^(2),y=0...

    Text Solution

    |

  7. Let f:[-1,2]vec[0,oo) be a continuous function such that f(x)=f(1-x)fo...

    Text Solution

    |

  8. Let S be the area of the region enclosed by y-e^(-x^(2)),y=0, x=0 and ...

    Text Solution

    |

  9. The value of the integral int(-pi//2)^(pi//2) (x^(2) + log" (pi-x)/(pi...

    Text Solution

    |

  10. Let f(x) = (1-x)^(2) sin^(2)x+ x^(2) for all x in IR and let g(x) = in...

    Text Solution

    |

  11. Let f(x) = (1-x)^(2) sin^(2)x+ x^(2) for all x in IR and let g(x) = in...

    Text Solution

    |

  12. If f(x) = int(0)^(x) e^(t^(2)) (t-2) (t-3) dt for all x in (0, oo) , t...

    Text Solution

    |

  13. The area enclosed by the curve y=sinx+cosxa n dy=|cosx-sinx| over the ...

    Text Solution

    |

  14. Let f:[1/2,1]vecR (the set of all real numbers) be a positive, non-con...

    Text Solution

    |

  15. For a epsilonR (the set of all real numbers) a!=-1, lim(n to oo) ((1^(...

    Text Solution

    |

  16. Let f:[a,b]to[1,oo) be a continuous function and let g:RtoR be defined...

    Text Solution

    |

  17. Let f:(0,oo)vecR be given by f(x)=int(1/x)^x(e^(-(t+1/t))dt)/t , then ...

    Text Solution

    |

  18. The value of int0^1 4x^3{(d^2)/(dx^2)(1-x^2)^5}dx is

    Text Solution

    |

  19. The following integral int(pi//4)^(pi//2)(2cosec x)^(17) dx dx is equa...

    Text Solution

    |

  20. Given that for each a epsilon(0,1),lim(hto 0^(+)) int(h)^(1-h)t^(-a)(1...

    Text Solution

    |