Home
Class 11
MATHS
If alpha, beta are the roots of x^(2) - ...

If `alpha, beta` are the roots of `x^(2) - px + q = 0` and `alpha', beta'` are the roots of `x^(2) - p' x + q' = 0`, then the value of `(alpha - alpha')^(2) + (beta + alpha')^(2) + (alpha - beta')^(2) + (beta - beta')^(2)` is

Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CENGAGE ENGLISH|Exercise All Questions|365 Videos

  • CONIC SECTIONS

    CENGAGE ENGLISH|Exercise All Questions|1344 Videos

Similar Questions

Explore conceptually related problems

If alpha and beta are the roots of 2x^(2) + 5x - 4 = 0 then find the value of (alpha)/(beta) + (beta)/(alpha) .

If alpha , beta are the roots of x^2-p(x+1)+c=0 then (1+alpha )( 1+ beta )=

If alpha and beta are the roots of x^2 - p (x+1) - c = 0 , then the value of (alpha^2 + 2alpha+1)/(alpha^2 +2 alpha + c) + (beta^2 + 2beta + 1)/(beta^2 + 2beta + c)

If alpha and beta are the roots of x^2 - p (x+1) - c = 0 , then the value of (alpha^2 + 2alpha+1)/(alpha^2 +2 alpha + c) + (beta^2 + 2beta + 1)/(beta^2 + 2beta + c)

If alpha , beta are the roots of x^2 +x+1=0 then alpha beta + beta alpha =

If alpha, beta are the roots of x^(2)+x+1=0 , then alpha^(-2)+beta^(-2) is

If alpha and beta be the roots of equation x^(2) + 3x + 1 = 0 then the value of ((alpha)/(1 + beta))^(2) + ((beta)/(1 + alpha))^(2) is equal to

If alpha, beta are the roots of x^(2) + 7x + 3 = 0 then (alpha – 1)^(2) + (beta – 1)^(2) =

If alpha and beta (alpha gt beta) are the roots of x^(2) + kx - 1 =0 , then find the value of tan^(-1) alpha - tan^(-1) beta

If alpha,beta be the roots of x^(2)-a(x-1)+b=0 , then the value of (1)/(alpha^(2)-a alpha)+(1)/(beta^(2)-a beta)+(2)/(a+b) is

CENGAGE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. Find the value of expression (cospi/2+i sin(pi/2))(cos(pi/(2^2))+i si...

    Text Solution

    |

  2. Solve for z , i.e. find all complex numbers z which satisfy |z|^2-2i z...

    Text Solution

    |

  3. If alpha, beta are the roots of x^(2) - px + q = 0 and alpha', beta' a...

    Text Solution

    |

  4. If a ,b are complex numbers and one of the roots of the equation x^2+a...

    Text Solution

    |

  5. If |z1|=|z2|=1, then prove that |z1+z2|= |1/z1+1/z2∣

    Text Solution

    |

  6. If (a x^2+c)y+(a^(prime)x^2+c^(prime) )=0 and x is a rational function...

    Text Solution

    |

  7. Find the principal argument of the complex number sin(6pi)/5+i(1+cos(6...

    Text Solution

    |

  8. For x in (0,1) , prove that i^(2i+3) ln((i^3x^2+2x+i)/(i x^2+2x+i^3))=...

    Text Solution

    |

  9. The sum of the non-real root of (x^2+x-2)(x^2+x-3)=12 is -1 b. 1 c. -...

    Text Solution

    |

  10. If n is a positive integer, prove that |I m(z^n)|lt=n|I m(z)||z|^(n-1....

    Text Solution

    |

  11. The number of roots of the equation sqrt(x-2)(x^2-4x+3)=0 is (A) Thre...

    Text Solution

    |

  12. If z1, z2a n dz3, z4 are two pairs of conjugate complex numbers, then ...

    Text Solution

    |

  13. Prove that following inequalities: |z/(|z|)-1|lt=|a rgz| (ii) |z-1|lt=...

    Text Solution

    |

  14. If x=1+i is a root of the equation =x^3-i x+1-i=0, then the other real...

    Text Solution

    |

  15. Find the modulus, argument, and the principal argument of the complex ...

    Text Solution

    |

  16. Find the principal argument of the complex number ((1+i)^5(1+sqrt(3i))...

    Text Solution

    |

  17. Column I, Column II: possible argument of z=a+i b a b >0 , p. tan^(...

    Text Solution

    |

  18. If the expression x^2+2(a+b+c)+3(b c+c+a b) is a perfect square, then ...

    Text Solution

    |

  19. Find the point of intersection of the curves a r g(z-3i)=(3pi)/4a n d ...

    Text Solution

    |

  20. The curve y=(lambda+1)x^2+2 intersects the curve y=lambdax+3 in exac...

    Text Solution

    |