Home
Class 12
MATHS
The four point A(a,0), B(b,0) ,C(c,0) an...

The four point `A(a,0), B(b,0) ,C(c,0) and D(d,0)` are such that a and b are the roots of the equation `p_(1)x^(2)+2q_(1)x+r_(1)=0 and c` and d are the roots of the equation `P_(2)x^(2)++2q_(2)+r_(2)=0`. Show that the sum of the equation `p_(2)x^(2)+2q_(2)x+r_(r)0`. Show that the sum of the ratios in which C and D divide AB is zero if `p_(1)r_(2)+p_(2)r_(1)=2q_(1)q_(2)`.

Promotional Banner

Topper's Solved these Questions

  • MISCELLANEOUS EXAMPLES

    CHHAYA PUBLICATION|Exercise COORDINATE GEOMETRY (THREE DIMENSIONAL COORDINATE GEOMETRY)|10 Videos

  • MISCELLANEOUS EXAMPLES

    CHHAYA PUBLICATION|Exercise CALCULUS|84 Videos

  • MISCELLANEOUS EXAMPLES

    CHHAYA PUBLICATION|Exercise ALGEBRA|141 Videos

  • METHOD OF SUBSTITUTION

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Examination (Assertion-Reason Type)|2 Videos

  • ORDER AND DEGREE OF DIFFERENTIAL EQUATION

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Examination (E Assertion - Reasion Type )|2 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 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 .

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

If the roots of the equation qx^2+2px+2q=0 are real and unequal, prove that the roots of the equation (p+q)x^2+2qx+(p-q)=0 are imaginary.

If p. q are odd integers. Then the roots of the equation 2px^(2)+(2p+q)x+q=0 are

Given that a,c are the roots of the equation px^2-3x+2=0 and b,d are the roots of the equation qx^2-4x+2=0 , find the values of p and q such that 1/a,1/b,1/c and 1/d are in A.P.

Express the roots of the equation q^2x^2-(p^2-2q)x+1=0 in terms of those of x^2+px+q=0 .

If the roots of the equation qx^2 + 2px + 2q =.0 are real and unequal then prove that the roots of the equation (p + q)x^2 + 2qx + (p - q)=0 are imaginary,

If the roots of the equation p(q-r)x^2+q(r-p)x+r(p-q)=0 be equal ,show that 1/p+1/r=2/q

CHHAYA PUBLICATION-MISCELLANEOUS EXAMPLES-COORDINATE GEOMETRY (TWO DIMENSIONAL COORDINATE GEOMETRY)
  1. Find the equation to the locus represented by the parametric equation...

    Text Solution

    |

  2. If t is a variable parameter, then the equation to the locus defined b...

    Text Solution

    |

  3. The four point A(a,0), B(b,0) ,C(c,0) and D(d,0) are such that a and b...

    Text Solution

    |

  4. The straight lines y=x=2 and y=6x+3 are parallel to two sides of the r...

    Text Solution

    |

  5. The eqution of the side BC,CA and AB of the triangle ABC are u(1)=a(1)...

    Text Solution

    |

  6. A striaght line intersect x-axis at A(7,0) and y-axis at B(0,-5). The ...

    Text Solution

    |

  7. The equation of two diameters of a circle of area 154 sq unit are 2x-3...

    Text Solution

    |

  8. If the four points (m(i),(1)/(m(i))) where m(1) gt 0 (I,1,2,3,4) are c...

    Text Solution

    |

  9. The ends A and B of a rod AB of length 8 unit slide along the lines y=...

    Text Solution

    |

  10. A is a point on the circle x^(2)+y^(2)=36. Find the locus of the point...

    Text Solution

    |

  11. The coordinates of the points A and B are (1,3) and (-2,1) respectivel...

    Text Solution

    |

  12. Find the equation of the diagonals of the parallelogram formed by the ...

    Text Solution

    |

  13. Show that the lines y=0, sqrt(3y)-xy=sqrt(3) and sqrt(3y)+x-10=0 form ...

    Text Solution

    |

  14. Prove analytically that the perpendicular bisector of the sides of a t...

    Text Solution

    |

  15. The coordinates of the vertex A of the triangle ABC are (-5,2) the equ...

    Text Solution

    |

  16. The coordinates of the vertices of a triangle are [at(1)t(2),a(t(1)+t(...

    Text Solution

    |

  17. Prove that diagonals of the parallelogram formed by the four straight ...

    Text Solution

    |

  18. Find the locus of the foot of the perpendicular from the origin upon ...

    Text Solution

    |

  19. Show that for all values of a,b and c the line (b-c)x+(c-a)y+a-b=0 alw...

    Text Solution

    |

  20. Show that the locus of the point of intersection of the stright lines ...

    Text Solution

    |