Home
Class 11
MATHS
Column I, Column II If x^2+a x+b=0 has...

Column I, Column II If `x^2+a x+b=0` has roots `alpha,betaa n dx^2+p x+q=0` has roots `alpha,gamma` , then, p. `(1-b q)^2=(a-p b)(p-a q)` If `x^2+a x+b=0` has roots `alpha,betaa n dx^2+p x+q=0` has roots `1//alpha,gamma` , then, q. `(4-b q)^2=(4a+2p b)(-2p-a q)` If `x^2+a x+b=0` has roots `alpha,betaa n dx^2+p x+q=0` has roots `2//alpha,gamma` , then, r. `(1-4b q)^2=(a+2p b)(-2p-4a q)` If `x^2+a x+b=0` has roots `alpha,betaa n dx^2+p x+q=0` has roots `1//(2alpha),gamma` , then, s. `(q-b)^2=(a q+b p)(p-a)`

Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CENGAGE PUBLICATION|Exercise All Questions|363 Videos

  • CONIC SECTIONS

    CENGAGE PUBLICATION|Exercise All Questions|1167 Videos

Similar Questions

Explore conceptually related problems

If p and q are the roots of the equation x^2+px+q =0, then

If , p , q are the roots of the equation x^(2)+px+q=0 , then

If sec alpha and cosec alpha are the roots of x^2-px+q=0 then prove that p^2=q(q+2)

Let alpha,beta in Rdot If alpha,beta^2 are the roots of quadratic equation x^2-p x+1=0. a n dalpha^2,beta are the roots of quadratic equation x^2-q x+8=0, then find p ,q,alpha,betadot

If the roots of the equation x^2-px+q=0 be alpha,beta and the roots of the equation x^2-ax+b=0 be alpha,1/beta then prove that, bq(a-p)^2=(q-b)^2 .

If sec alpha and alpha are the roots of x^2-p x+q=0, then (a) p^2=q(q-2) (b) p^2=q(q+2) (c) p^2q^2=2q (d) none of these

If the roots of the equation (x - p) (x - q) -r = 0 are alpha , beta then the roots of the equation (y - beta) (y - alpha) + r = 0 are

If sec alpha and "cosec" alpha are the roots of x^(2)- px+q=0 then show that p^(2)=q(q+2)

If p(q-r)x^2+q(r-p)x+r(p-q)=0 has equal roots, then prove that 2/q=1/p+1/rdot

IF alpha and beta be the roots of the equation x^2+px+q=0 show that alpha/beta is a root of the equation qx^2-(p^2-2q)x+q=0 .

CENGAGE PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. Let a is a real number satisfying a^3+1/(a^3)=18 . Then the value of a...

    Text Solution

    |

  2. Find non zero integral solutions of |1-i|^x=2^xdot

    Text Solution

    |

  3. Column I, Column II If x^2+a x+b=0 has roots alpha,betaa n dx^2+p x+...

    Text Solution

    |

  4. If (1+i)(1+2i)(1+3i)......(1+n i)=(x+i y) , show that 2. 5. 10...... (...

    Text Solution

    |

  5. If a x^2+b x+c=0,a ,b ,c in R has no real zeros, and if c<0 , then wh...

    Text Solution

    |

  6. If omega is a cube root of unity, then find the value of the following...

    Text Solution

    |

  7. If f(x)=sqrt(x^2+a x+4) is defined for all x , then find the value of ...

    Text Solution

    |

  8. If omega is a cube root of unity, then find the value of the following...

    Text Solution

    |

  9. Find the domain and range of f(x)=sqrt(x^2-4x+6)

    Text Solution

    |

  10. Prove that |z1+z2|^2=|z1|^2+|z2|^2, ifz1//z2 is purely imaginary.

    Text Solution

    |

  11. Find the range of the function f(x)=6^x+3^x+6^(-x)+e^(-x)+2.

    Text Solution

    |

  12. If omega is a cube root of unity, then find the value of the following...

    Text Solution

    |

  13. If alpha ,beta are the roots of the equation 2x^2+2(a+b)x+a^2+b^2=0 th...

    Text Solution

    |

  14. Let z1,z2, z3,......, zn be complex numbers such that |z1|=|z2|=...=|z...

    Text Solution

    |

  15. If a ,b , in R such that a+b=1a n d(1-2ab)(a^3+b^3)=12 . The value ...

    Text Solution

    |

  16. If |z|lt=4 , then find the maximum value of |i z+3-4i|dot

    Text Solution

    |

  17. Find the range of f(x)=x^2-x-3.

    Text Solution

    |

  18. If the fraction (x^3 +(a-10)x^2-x+a-6)/(x^3 +(a-6)x^2-x+a-10)reduces t...

    Text Solution

    |

  19. The polynomial f(x)=x^4+a x^3+b x^3+c x+d has real coefficients and f(...

    Text Solution

    |

  20. Find the value of i^n+i^(n+1)+i^(n+2)+i^(n+3) for all n in Ndot

    Text Solution

    |