Home
Class 12
MATHS
Let X1, X2, x3 be 3 roots of the cubic...

Let` X_1, X_2, x_3 ` be `3` roots of the cubic ` x^3 – X-1 = 0. ` Then the expression ` x_1(x_2 - X_3)^2 + x_2 (x_3 - x_1)^2 + x_3(x_1 - x_2)^2` equals a rational number.Find the absolute value of the number.

Text Solution

Verified by Experts

The correct Answer is:
9
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRATION & ITS APPLICATION

    RESONANCE|Exercise High Level Problem|37 Videos

  • EQUATIONS

    RESONANCE|Exercise EXERCISE-2 (PART-II: PREVIOUSLY ASKED QUESTION OF RMO) |7 Videos

Similar Questions

Explore conceptually related problems

If x^2 - 3x + 1 = 0 , then the value of (x^6 + x^4 + x^2 + 1)/(x^3) will be

Let x_1, x_2, x_3 be the roots of equation x^3-x^2+beta x+gamma=0 . If , x_1,x_2,x_3 are in A.P. then

let x_(1),x_(2),x_(3) be the roots of equation x^(3)+3x+5=0 what is the value of the expression (x_(1)+(1)/(x_(1)))(x_(2)+(1)/(x_(2)))(x_(3)+(1)/(x_(3)))=?

Let x_(1),x_(2),x_(3) bet the roots of equation x^(3) - x^(2) +betax + gamma = 0 If x_(1),x_(2),x_(3) are in A. P ., then

(log (x^(3) + 3x^(2) + 3x + 1))/(log (x^(2) + 2x + 1)) is equal to

RESONANCE-DPP-QUESTION
  1. If both roots of the equation a(x^2-1)+x+c are imaginary and c gt -1 t...

    Text Solution

    |

  2. Find the number of integral values of 'a' for which ax^2 - (3a + 2)x +...

    Text Solution

    |

  3. Let X1, X2, x3 be 3 roots of the cubic x^3 – X-1 = 0. Then the exp...

    Text Solution

    |

  4. for all x in R if mx^2-9mx+5m+1gt0 then m lies in the interval

    Text Solution

    |

  5. If the difference between the corresponding roots of x^(2)+ax+b=0and x...

    Text Solution

    |

  6. The number of roots of the equation, x-(2)/(x-1) is

    Text Solution

    |

  7. If sin thetaand cos theta are the roots of the equation ax^(2)-bx+c=0,...

    Text Solution

    |

  8. Number of integral value (s) of 'x' satisfying the equation log(1/5)(s...

    Text Solution

    |

  9. The set (A uu B')uu(B nn C) is equal to

    Text Solution

    |

  10. The set (A uu B')uu(B nn C) is equal to

    Text Solution

    |

  11. If n(AuuBuuC)+n(AuuBuuC)'=50,n(A)=10,n(B)=15,n(C)=20,n(AnnB)=5,n(BnnC)...

    Text Solution

    |

  12. If A={2,3,4,8,10}.B={3,4,5,10,12},C={4,56,12,14}then(AnnB)uu(AnnC) is ...

    Text Solution

    |

  13. If A={1,3,5,7,9,11,13,15,17}, B={2,4,.......,18} and N the set of natu...

    Text Solution

    |

  14. Of the number of three athletic teams in a school, 21 are in the baske...

    Text Solution

    |

  15. Find the value of a for which the sum of the squares of the roots of t...

    Text Solution

    |

  16. The graph of the quadratic trinomial u=a x^2+b x+c has its vertex at (...

    Text Solution

    |

  17. If a, b, c are real numbers satisfying the condition a+b+c=0 then the ...

    Text Solution

    |

  18. The quadratic equation whose roots are sec^(2)alphaand "cosec"^(2)alph...

    Text Solution

    |

  19. If h(x)=log(10)x, then the value of sum(n=1)^(89) h"("tan^(Omega)")"=

    Text Solution

    |

  20. Let f(n)=prod(f=1)^(n) sin(r), where r is in radians, then

    Text Solution

    |