Home
Class 11
MATHS
If roots of the equation x^2-10cx-11d=0 ...

If roots of the equation `x^2-10cx-11d`=0 are a,b and those of `x^2-10ax-11b`=0 are c,d,then the sum of the digits of a+b+c+d must be equal to (a,b,c and d are distinct numbers)

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 the roots of the equation a(b-c)x^2+b(c-a)x+c(a-b)=0 are equal,then a,b,c are in

If the equation x^2-cx+d=0 and x^2-ax+b=0 have a common root,and the roots of the second equations are equal ,then prove that 2(b+d)=ac

If the roots of the equation x^2+a x+b=0 are c and d , then roots of the equation x^2+(2c+a)x+c^2+a c+b=0 are a c b. d-c c. 2c d. 0

If the roots of the equation a(b-c)x^2+b(c-a)x+c(a-b)=0 are equal, show that 2//b=1//a+1// c dot

If the roots of the quadratic equation (b-c)x^2+(c-a)x+(a-b)= 0 are equal, then prove that 2b=a+c.

If 1,2,3 and 4 are the roots of the equation x^4+ax^3+bx^2+cx+d =0 then a+2b+c=

If the sum of the roots of the quadratic equation a x^2+b x+c=0 is equal to the sum of the squares of their reciprocals, then prove that a/c , b/a a n d c/b are in H.P.

If 2 + i and sqrt5-2i are the roots of the equation (x^2+ax+b)(x^2+cx+d)=0 , where a,b,c,d are real constants, then product of all roots of the equation is

If c ,d are the roots of the equation (x-a)(x-b)-k=0 , prove that a, b are roots of the equation (x-c)(x-d)+k=0.

If the roots of the quadratic equation (a^2+b^2)x^2-2(ac+bd)x+(c^2+d^2)=0 are equal, prove that a/b=c/d .

CENGAGE PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. If a ,b ,c ,d are four consecutive terms of an increasing A.P., then t...

    Text Solution

    |

  2. Find the relation if z1, z2, z3, z4 are the affixes of the vertices of...

    Text Solution

    |

  3. If roots of the equation x^2-10cx-11d=0 are a,b and those of x^2-10ax-...

    Text Solution

    |

  4. If z1, z2, z3 are three nonzero complex numbers such that z3=(1-lambda...

    Text Solution

    |

  5. Coefficient of x^99 in the polynomial (x-1) (x-2)....(x-100) is

    Text Solution

    |

  6. Let z1, z2, z3 be three complex numbers and a ,b ,c be real numbers no...

    Text Solution

    |

  7. Fill in the blanks If 2+isqrt(3) is a root of the equation x^2+p x+q=0...

    Text Solution

    |

  8. Prove that the triangle formed by the points 1,(1+i)/(sqrt(2)),a n di ...

    Text Solution

    |

  9. Fill in the blanks. If the product of the roots of the equation x^2-3k...

    Text Solution

    |

  10. Solve for z : z^2-(3-2i)z=(5i-5)dot

    Text Solution

    |

  11. If the equations x^2+ax+b=0 and x^2+bx+a=0 have one common root. Then ...

    Text Solution

    |

  12. Find all possible values of sqrt(i)+sqrt(-i)dot.

    Text Solution

    |

  13. Fill in the blanksIfx<0,y<0,x+y+(x//y)=(1//2)a n d (x+y)(x//y)=-(1//2...

    Text Solution

    |

  14. Find the square roots of the following: (i) 7-24 i

    Text Solution

    |

  15. True or false The equation2x^2+3x+1=0 has an irrational root.

    Text Solution

    |

  16. If z!=0 is a complex number, then prove that R e(z)=0 rArr Im(z^2)=0.

    Text Solution

    |

  17. If l ,m ,n are real and l!=m , then the roots of the equation (l-m)x...

    Text Solution

    |

  18. Let z be a complex number satisfying the equation z^2-(3+i)z+m+2i=0\ ,...

    Text Solution

    |

  19. If x ,y and z are real and different and u=x^2+4y^2+9z^2-6y z-3z x-2x ...

    Text Solution

    |

  20. If (x+i y)^3=u+i v , then show that u/x+v/y=4(x^2-y^2)

    Text Solution

    |