Home
Class 12
MATHS
Let alpha be a repeated root of a qua...

Let `alpha` be a repeated root of a quadratic equation `f(x)=0a n dA(x),B(x),C(x)` be polynomials of degrees 3, 4, and 5, respectively, then show that `|A(x)B(x)C(x)A(alpha)B(alpha)C(alpha)A '(alpha)B '(alpha)C '(alpha)|` is divisible by `f(x)` , where prime `(')` denotes the derivatives.

Promotional Banner

Topper's Solved these Questions

  • DETERMINANT

    CENGAGE|Exercise Multiple Correct Answer|5 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE|Exercise Exercise|337 Videos

Similar Questions

Explore conceptually related problems

If alpha and beta are the roots of the quadratic equcation x^(2)+sqrt2x+3=0 , form a quadratic polynomial with zeroes 1/alpha,1/beta .

If alpha and beta are the roots of quadratic equation 2x^(2)+4x+3=0 , then the value of alpha+beta= A)-2 B)2 C)34 D)-4

If alpha" and "beta are the roots of the equation x^(2)+3x-4=0 , then (1)/(alpha)+(1)/(beta) is equal to

If alpha and beta are the roots of the equation x^(2)-ax+b=0 ,find Q(b) (1)/(alpha)+(1)/(beta)

sin 3 alpha = 4 sin alpha sin(x + alpha) sin(x-alpha)

If alpha and beta are the roots of the equation x^(2)-ax+b=0 ,find Q (a)(alpha)/(beta)+(beta)/(alpha)

If alpha and beta are the roots of the quadratic equation x^(2) + sqrt(2x) + 3 = 0 . Form a quadratic polynomial with zeros (1)/(alpha), (1)/(beta) .

If alpha" and "beta are the roots of the quadratic equation 4x^(2)+3x+7=0 , then the value of (1)/(alpha)+(1)/(beta)=

If alpha, beta are the roots of the equation (x-a)(x-b)=5 then the roots of the equation (x- alpha)(x-beta)+5=0 are

CENGAGE-DETERMINANTS-All Questions
  1. f(x)=|cos xx1 2sinxx^2 2xtanxx1| . Then value of (lim)(xvec0)(f(x))/x ...

    Text Solution

    |

  2. If the system of linear equation x + 2ay + az = 0, x + 3by + bz = 0, x...

    Text Solution

    |

  3. Let alpha be a repeated root of a quadratic equation f(x)=0a n dA(x...

    Text Solution

    |

  4. If |a^2+lambda^2a b+clambdac a-blambdaa b-clambdab^2+lambda^2b c+...

    Text Solution

    |

  5. Value of |1+x1 1+x1x1+x1x^2 1+x2 1+x2x1+x2x^2 1+x3 1+x3x1+x3x^2| depen...

    Text Solution

    |

  6. If (x)=|alpha+xtheta+xlambda+xbeta+xvarphi+xmu+xgamma+xpsi+x v+x| show...

    Text Solution

    |

  7. The value of determinant |b c-a^2a c-b^2a b-c^2a c-b^2a b-c^2b c-a^2a ...

    Text Solution

    |

  8. The value of the determinant (a1-b1)^2(a1- ...

    Text Solution

    |

  9. If l1^2+m1^2+n1^2=1 etc., and l1 l2+m1 m2+n1 n2 = 0, etc. and Delta...

    Text Solution

    |

  10. Integrate (sinx)/((sinx-cosx))dx=?

    Text Solution

    |

  11. The value of determinant |[ ^n C(r-1), ^n Cr, (r+1)^(n+2)C(r+1)],[ ^n...

    Text Solution

    |

  12. Let |{:(x,,2,,x),(x^(2),,x,,6),(x,,x,,6):}|=Ax^(4) +Bx^(3)+Cx^(2)+Dx+E...

    Text Solution

    |

  13. Let a ,b , c be the real numbers. The following system of equations in...

    Text Solution

    |

  14. The value of the determinant |[sintheta, costheta, sin2theta] , [sin(t...

    Text Solution

    |

  15. Find the value of the determinant |b cc a a b p q r1 1 1|,w h e r ea ,...

    Text Solution

    |

  16. let a > 0 , d > 0 find the value of the determinant |[1/a,1/(a(a + d))...

    Text Solution

    |

  17. For all values of A,B,C and P,Q,R show that |{:(cos(A-P),,cos(A-Q)...

    Text Solution

    |

  18. Let lambdaa n dalpha be real. Find the set of all values of lambda for...

    Text Solution

    |

  19. Prove that |a x-b y-c z a y+b x c x+a z a y+b x b y-c z-a x b z+c y c...

    Text Solution

    |

  20. If (x)=|alpha+xtheta+xlambda+xbeta+xvarphi+xmu+xgamma+xpsi+x v+x| show...

    Text Solution

    |