Home
Class 11
MATHS
If the ratio of the roots of the equatio...

If the ratio of the roots of the equation `x^2+p x+q=0` are equal to ratio of the roots of the equation `x^2+b x+c=0` , then prove that `p^2c=b^2qdot`

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 the ratio of the roots of the equation x^2+p x+q=0 are equal to ratio of the roots of the equation x^2+b x+c=0 , then prove that p^(2)c=b^2qdot

If the ratio of the roots of the equation ax^2+bx+c=0 is equal to ratio of roots of the equation x^2+x+1=0 then a,b,c are in

If the ratio of the roots of the equation x^(2)+px+q=0 is equal to the ratio of the roots of x^(2)+lx+m=0 , prove that mp^(2)=ql^(2) .

If p + iq be one of the roots of the equation x^(3) +ax +b=0 ,then 2p is one of the roots of the equation

if the difference of the roots of the equation x^(2)+ ax +b=0 is equal to the difference of the roots of the equation x^(2) +bx +a =0 ,then

If the ratio of the roots of x^(2) + bx + c = 0 is equal to the ratio of the roots of x^(2)+px+q=0 , then p^(2)c-b^(2)q=

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

The roots of a_1x^2+b_1x + c_1=0 are reciprocal of the roots of the equation a_2x^2 +b_2x+c_2=0 if

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

The roots of the equation (b-c) x^2 +(c-a)x+(a-b)=0 are

CENGAGE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. Let a be a complex number such that |a|<1a n dz1, z2,z3,... be the ve...

    Text Solution

    |

  2. Let lambda in R . If the origin and the non-real roots of 2z^2+2z+lam...

    Text Solution

    |

  3. If the ratio of the roots of the equation x^2+p x+q=0 are equal to rat...

    Text Solution

    |

  4. Let z=1-t+isqrt(t^2+t+2), where t is a real parameter.the locus of the...

    Text Solution

    |

  5. If sintheta,costheta be the roots of a x^2+b x+c=0 , then prove that b...

    Text Solution

    |

  6. Express the following complex numbers in a+i b form: ((3-2i)(2+3i))/((...

    Text Solution

    |

  7. If a ,b ,c are nonzero real numbers and a z^2+b z+c+i=0 has purely i...

    Text Solution

    |

  8. If z^2+z|z|+|z^2|=0, then the locus z is a. a circle b. a straight ...

    Text Solution

    |

  9. If the sum of the roots of the equation 1/(x+a)+1/(x+b)=1//c is zero,...

    Text Solution

    |

  10. Solve the equation x^2+p x+45=0. it is given that the squared differen...

    Text Solution

    |

  11. Find the least positive integer n such that ((2i)/(1+i))^n is a positi...

    Text Solution

    |

  12. z1a n dz2 lie on a circle with center at the origin. The point of inte...

    Text Solution

    |

  13. If alpha,beta are the roots of the equation 2x^2-35x+2=0 , the find ...

    Text Solution

    |

  14. If one root of the equation z^2-a z+a-1= 0 is (1+i), where a i...

    Text Solution

    |

  15. If |z1|=|z2|=|z3|=1 and z1+z2+z3=0 then the area of the triangle whose...

    Text Solution

    |

  16. Simplify: (sqrt(5+12 i)+sqrt(5-12 i))/(sqrt(5+12 i)-sqrt(5-12 i))

    Text Solution

    |

  17. Find a quadratic equation whose product of roots x1 and x2 is equa...

    Text Solution

    |

  18. If sqrt(5-12 i)+sqrt(-5-12 i)=z , then principal value of a rgz can be

    Text Solution

    |

  19. If (x+i y)(p+i q)=(x^2+y^2)i , prove that x=q ,y=pdot

    Text Solution

    |

  20. If a and b(!=0) are the roots of the equation x^2+a x+b=0, then find...

    Text Solution

    |