Home
Class 10
MATHS
If alpha, beta, gamma are the zeros of t...

If `alpha, beta, gamma` are the zeros of the polynomial `f(x) = ax^(3) + bx^(2) + cx + d` then `(alpha)^2 + (beta)^2 + (gamma)^2` = ………….

A

`(b^(2) + 4ac)/(2)`

B

`(b^(2) - 2ac)/(a^2)`

C

`(b + 2ac)/(a^2)`

D

none

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • POLYNOMIALS

    VGS PUBLICATION-BRILLIANT|Exercise EXERCISE|244 Videos
  • POLYNOMIALS

    VGS PUBLICATION-BRILLIANT|Exercise Part - B : Observation bits to solve various bits given in the public examination.|40 Videos
  • PAIR OF LINEAR EQUATIONS IN TWO VARIABLES

    VGS PUBLICATION-BRILLIANT|Exercise EXERCISE|262 Videos
  • PROBABILITY

    VGS PUBLICATION-BRILLIANT|Exercise EXERCISE|220 Videos

Similar Questions

Explore conceptually related problems

If alpha, beta, gamma are the zeros of the polynomial f(x) = ax^(3) + bx^(2) + cx + d then 1/(alpha) + 1/(beta) + 1/(gamma) = ………….

If alpha, beta , gamma are the zeros of the polynomial x^(3) - px^(2) + qx - r then 1/(alpha beta) + 1/(beta gamma) + 1/(gamma alpha) = …………..

If alpha, beta are the zeros of the polynomial f(x) = ax^(2) + bx + c then 1/(alpha^2) + 1/(beta^2) = …………….

If alpha, beta, gamma are the zeroes of the cubic polynomial ax^(3) + bx^(2) + cx +d and (a != 0) , then alpha beta gamma = ……….

If alpha, beta, gamma are the roots of the equation x^(3) - ax^(2) + bx -c = 0 , then sum alpha^(2) (beta + gamma)=

If alpha, beta, gamma are the roots of x^(3) + x^(2) + x + 1 = 0 then (alpha - beta)^(2) + (beta - gamma)^(2) + (gamma - alpha)^(2) =

Match of the following : If alpha, beta , gamma are zeroes of a cubic polynomial ax^(3) + bx^(2) + cx + d , (a != 0) , then ………. {:((i) alpha+beta +gamma, (a) -d/a),((ii) alphabeta +betagamma+gamma alpha, (b) c/a),((iii) alphabeta gamma, (c) -b/a):}

If alpha, beta, gamma are the roots of the equation x^(3) - 6x^(2) + 11x - 6 = 0 and if a = alpha^(2) + beta^(2) + gamma^(2) , b = alpha beta + beta gamma + gamma alpha and c = (alpha + beta) (beta + gamma)(gamma + alpha), then the correct inequality among the following is :

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

If alpha, beta, gamma are the roots of x^(3) + x^(2) + x + 1 = 0 then alpha^(2) + beta^(2) + gamma^(2) =

VGS PUBLICATION-BRILLIANT-POLYNOMIALS-Creative Bits for CCE Model Examination
  1. If alpha, beta are the zeros of polynomial f(x) = x^(2) - p(x+1)-c the...

    Text Solution

    |

  2. If the sum of the zeros of the polynomial f(x) = 2x^(3) - 3 kx^(2) + 4...

    Text Solution

    |

  3. If alpha, beta, gamma are the zeros of the polynomial f(x) = ax^(3) + ...

    Text Solution

    |

  4. If the polynomial f(x) = ax^(3) + bx - c is divisible by the polynomi...

    Text Solution

    |

  5. The product of the zeros of x^(3) + 4x^(2) + x - 6 is ………….

    Text Solution

    |

  6. A quadratic polynomial , the sum of whose zeroes of 0 and one zero is ...

    Text Solution

    |

  7. If sqrt(5) and -sqrt(5) are two zeros of the polynomial x^(3) + 3x^(2)...

    Text Solution

    |

  8. If alpha, beta , gamma are the zeros of the polynomial x^(3) - px^(2) ...

    Text Solution

    |

  9. If x+ 2 is a factor of x^(2) + ax + 2b and a+b = 4 then a = …………..

    Text Solution

    |

  10. In the above problem b = ……………..

    Text Solution

    |

  11. If one zero of the polynomial f(x) = (k^(2)+4)x^(2) + 13 x + 4k is rec...

    Text Solution

    |

  12. If two zeros of x^(3) + x^(2) - 5x -5 are sqrt(5) and -sqrt(5) then it...

    Text Solution

    |

  13. If zeros of polynomial f(x0 = x^(3) - 3px^(2)+qx-r are in AP then 2p^(...

    Text Solution

    |

  14. If alpha, beta are the zeros of the polynomial f(x) = ax^(2) + bx + c ...

    Text Solution

    |

  15. What should be subtracted from the polynomial x^(2) - 16x + 30 so that...

    Text Solution

    |

  16. From the graph the number of zeros of the polynomial is ………………

    Text Solution

    |

  17. The number of zeros of the polynomial in the graph is …………

    Text Solution

    |

  18. The number of zeros of the polynomial in the graph is ………….

    Text Solution

    |

  19. The below graph represents

    Text Solution

    |

  20. The graph represents …………..

    Text Solution

    |