Home
Class 12
MATHS
Find the sum of the squares of the roots...

Find the sum of the squares of the roots of `ax^4+bx^3+cx^2+dx+e = 0 , a ne 0`.

Text Solution

Verified by Experts

The correct Answer is:
`(b^2-2ac)/a^2`
Promotional Banner

Topper's Solved these Questions

  • THEORY OF EQUATIONS

    FULL MARKS|Exercise EXERCISE 3.1|12 Videos

  • THEORY OF EQUATIONS

    FULL MARKS|Exercise EXERCISE 3.2|5 Videos

  • SAMPLE PAPER-09 (UNSOLVED)

    FULL MARKS|Exercise PART-IV (IV. Answer all the questions. )|15 Videos

  • TWO DIMENSIONAL ANALYTICAL GEOMETRY-II

    FULL MARKS|Exercise Additional Question Solved|44 Videos

Similar Questions

Explore conceptually related problems

Find the sum of the squares of the roots of 3x^3-2x^2+4x+1=0

Find the sum of squares of roots of the equation 2x^4 - 8x^3 + 6x^2 - 3=0

Find the condition that the roots of ax^3+bx^2+cx+d=0 are in H.P.

If the sum of the roots of the quadratic equation ax^2 + bx + c = 0 ( abc ne 0) is equal to the sum of the squares of their reciprocals, the sum of the squares of their reciprocals, then a/c , b/a , c/b are in H.P.

One of the roots of ax^(2) + bx + c = 0 is greater than 2 and the other is less than -1. If the roots of cx^(2) + bx + a = 0 are alpha and beta , then

Find the value of k for which the sum of the squares of the reciprocals of the roots of x^(2)+kx+9=0is(2)

If the sum of the roots of the quadratic equation ax^(2)+bx+c=0 is equal to the sum of the squares of their reciprocals, then (a)/(c ), (b)/(a)" and "(c )/(b) are in

Find the condition that the roots of the equation ax^3+bx^2+cx+d=0 are in A.P.

FULL MARKS-THEORY OF EQUATIONS -Additional Questions Solved
  1. Find the sum of the squares of the roots of ax^4+bx^3+cx^2+dx+e = 0 , ...

    Text Solution

    |

  2. Construct a cubic equation with roots 2,3,4.

    Text Solution

    |

  3. If alpha, beta and gamma are the cubic equation x^3-6x^2+11x-6=0. From...

    Text Solution

    |

  4. If the roots of x^4+5x^3-30x^2-40x+64=0 are in G. P , then find the ro...

    Text Solution

    |

  5. Determine the value of k such that the equation (2k-5)x^2-4x-15=0 and ...

    Text Solution

    |

  6. If alpha, beta , gamma are the roots of the equation x^3+px^2+qx+r=0 ....

    Text Solution

    |

  7. alpha , beta , gamma are the roots of the equation x^3+3x^2+2x+1=0 . F...

    Text Solution

    |

  8. Find a polynomial equation of minimum degree with rational coefficient...

    Text Solution

    |

  9. Find a polynomial equation of minimum degree with rational co - effici...

    Text Solution

    |

  10. If the roots of equation x^3+px^2+qx+r=0 are in A.P then show that 2p...

    Text Solution

    |

  11. Solve 27x^3+42x^2-28x-8=0 given that its roots are in geometric progre...

    Text Solution

    |

  12. Solve the equation 15x^3-23x^2+9x-1=0 . Where roots are in H . P

    Text Solution

    |

  13. If one root of x^3+2x^2+3x+k=0 is sum of the other two roots then find...

    Text Solution

    |

  14. If sum of the roots of the equation x^3-3x^2-16x+k=0 is zero then find...

    Text Solution

    |

  15. Find all zeros of the polynomial x^3-5x^2-9x-5=0 , If 2 + I is a root.

    Text Solution

    |

  16. Solve (x-3)(x-6)(x-1)(x+2)+54=0

    Text Solution

    |

  17. Solve the equation (x-4)(x-2)(x-1)(x+1)+8=0

    Text Solution

    |

  18. Solve : 3^(2x+4)+1=2.3^(x+2)

    Text Solution

    |

  19. Solve : 2^(2x)-2^(2x+3)+2^4=0

    Text Solution

    |

  20. Solve (x-4)(x+2)(x+3)(x-3)+8=0

    Text Solution

    |

  21. Solve : (x+y)^(2//3)+2(x-y)^(2//3)=3(x^2-y^2)^(1//3) and 3x-2y=13.

    Text Solution

    |