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 ENGLISH|Exercise High Level Problem|26 Videos

  • EQUATIONS

    RESONANCE ENGLISH|Exercise EXERCISE-2 (PART-II: PREVIOUSLY ASKED QUESTION OF RMO) |5 Videos

Similar Questions

Explore conceptually related problems

If x_1, x_2, x_3,........x_n are the roots of x^n + ax + b = 0 , then the value of (x_1 - x_2)(x_1 - x_3) (x_1 - x_4) .......(x_1 – x_n) is equal to

Let x_(1),x_(2), x_(3) be 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 and x_2 be the real roots of the equation x^2 -(k-2)x+(k^2 +3k+5)=0 then the maximum value of x_1^2+x_2^2 is

If x_1, x_2 be the roots of the equation x^2 -3x+ A=0 and x_3,x_4 be those of the equation x^2-12x + B = 0 and x_1 , x_2, x_3, x_4 be an increasing GP. find find A and B.

If the expression |{:(x^2+x+3,1,4),(2x^4+x^3+2x+1,2,3),(x^2+x,1,1):}| is equal to ax^4+bx^3+cx^2+dx+e , then the value of e is equal to

The number of solution of the following equations x_2 - x_3 = 1, -x_1 + 2x_3 = -2, x_1 - 2x_2 = 3 is

Find the sum of the following algebraic expressions : 3x^(3) - 5x^(2) + 2x + 1 , 3x - 2x^(3) - x^(3) , 2x^(2) - 7x + 9

The number of solutions of x_1 + x_2 + x_3 = 51 (X1, X2, X3 being odd natural numbers) is

Let x_1,x_2 be the roots of the equation x^2-3x+A=0 and x_3,x_4 be those of equation x^2-12x+B=0 and x_1,x_2,x_3,x_4 form an increasing G.P. find A and B.

lim _ ( x to 2 ) ( 3 ^(x) + 3 ^( 3 - x ) - 12 ) /( 3 ^( - x//2) - 3 ^( 1 -x)) is equal to __________

RESONANCE ENGLISH-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 (AnnB')'uu(BnnC) 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 members of three athletic teams in a certain school, 21 are in ...

    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(r=1)^(n) sin(r), where r is in radians, then

    Text Solution

    |