Home
Class 12
MATHS
Prove that if the equations x^2+px+r=0 a...

Prove that if the equations `x^2+px+r=0` and `x^2+rx+p=0` have a common root then either p=r or , 1+p+r=0.

Promotional Banner

Topper's Solved these Questions

  • QUADRATIC EQUATIONS

    CHHAYA PUBLICATION|Exercise EXERCISE 5A(Long Answer type question)|56 Videos

  • QUADRATIC EQUATIONS

    CHHAYA PUBLICATION|Exercise EXERCISE 5B(Multiple Choice type question)|5 Videos

  • QUADRATIC EQUATIONS

    CHHAYA PUBLICATION|Exercise EXERCISE 5A(Very Short Answer type Question)|30 Videos

  • PROPERTIES OF TRIANGLE

    CHHAYA PUBLICATION|Exercise Assertion- Reason Type:|2 Videos

  • QUESTION PAPER -2018

    CHHAYA PUBLICATION|Exercise WBJEE|45 Videos

Similar Questions

Explore conceptually related problems

Prove that, if the equations x^2+px+qr=0 and x^2+qx+pr=0[pneq,rne0] have a common root , then p+q+r=0.

Show that the equations px^2+qx+r=0 and qx^2+px+r=0 will have a common root if p+q+r=0 or, p=q=r.

If the equation x^2+px+qr=0 and x^2+qx+pr=0(p!=q,r!=0) has same root then prove that p+q+r=0

If p, q, r are in G.P and the equation px^2+2qx+r=0 and dx^2+2ex+f=0 have a common root, then show that d/p, e/q, f/r are in AP.

If x^2+p x+q=0a n dx^2+q x+p=0,(p!=q) have a common roots, show that 1+p+q=0 .

If the equation x^2+px+q=0 and x^2+p'x+q'=0 have a common root , prove that , it is either (pq'-p'q)/(q'-q) or, (q'-q)/(p'-p) .

In the equation x^2-px+q=0 one root is twice of other then prove that 2p^2=9q

If one of the root of the equation px^2 + qx + r = 0 is the cube of the other, prove that. rp(r + p)^2 = (q^2 - 2rp)^2 .

If the roots of the equation x^2+2px+q=0 and x^2+2qx+p=0 where p!=q .Differ by a constant ,prove that p+q+1=0

In the equation x^2-px+q=0 ratio of the roots are 2:3 ,then prove that 6p^2=25q

CHHAYA PUBLICATION-QUADRATIC EQUATIONS-EXERCISE 5A(Short answer type question)
  1. Find the condition so that the roots of the equation a/(x-a)+b/(x-b)=5...

    Text Solution

    |

  2. Show that the roots of each of the following equations are rational(a,...

    Text Solution

    |

  3. Show that the roots of each of the following equations are rational(a,...

    Text Solution

    |

  4. Show that the roots of the equation (a^2-bc)x^2+2(b^2-ca)x+c^2-ab=0 ar...

    Text Solution

    |

  5. If one root of the equation qx^2+px+q=0 (p,q are real) be imaginary, s...

    Text Solution

    |

  6. If the roots of the equation qx^2+2px+2q=0 are real and unequal, prove...

    Text Solution

    |

  7. If the roots of the equation x^2-2(a+b)x+a(a+2b+c)=0 be equal , prove ...

    Text Solution

    |

  8. If the equation x^2+px+q=0andx^2+p'x+q'=0 have a common root , prove t...

    Text Solution

    |

  9. Prove that if the equations x^2+px+r=0 and x^2+rx+p=0 have a common ro...

    Text Solution

    |

  10. IF x is real and the expressions 3x^2-17x+20 is always positive, show ...

    Text Solution

    |

  11. Find the limits of real value of x so that the expressions 5x^2+6x-8 i...

    Text Solution

    |

  12. For any real positive value of x, show that 3-xcancelgt7/(x+2).

    Text Solution

    |

  13. If x is real can the value of 3+2x-x^2 be greater than 4,

    Text Solution

    |

  14. If x is real can that of x^2+3x+1 less than (-5/4)?

    Text Solution

    |

  15. Show that if x is real and x^2+5lt6x , then x must lie between 1 and ...

    Text Solution

    |

  16. If x is real, find the real values of p which make 4x^2+px+1 always p...

    Text Solution

    |

  17. IF x is real, find the real values of m which make the expressions mx-...

    Text Solution

    |

  18. If ((x-5)(x^2-2x+1))/((x-7)(x^2+2x+3)) is positive for all real values...

    Text Solution

    |

  19. If the equation y^2+x^2-10x+21=0 is satisfied by real values of x and ...

    Text Solution

    |

  20. If x is real , show that (x-2)(x-3)(x-4)(x-5)+2 is always positive.

    Text Solution

    |