Home
Class 12
MATHS
If x^(2) + ax + 1 is a factor of ax^(3)...

If `x^(2) + ax + 1 ` is a factor of `ax^(3) + bx + c,` them find the conditions.

A

`c^3=ab^3`

B

`a^3=bc^3`

C

`a^3=b^3c`

D

`b^3=ca^3`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • THEORY OF EQUATIONS

    PREMIERS PUBLISHERS|Exercise Problems for practice (Answer the following)|21 Videos

  • THEORY OF EQUATIONS

    PREMIERS PUBLISHERS|Exercise Exercise 3.7|10 Videos

  • PROBABILITY DISTRIBUTIONS

    PREMIERS PUBLISHERS|Exercise PROBLEMS FOR PRACTICE|40 Videos

  • TWO DIMENSIONAL ANALYTICAL GEOMETRY - II

    PREMIERS PUBLISHERS|Exercise PROBLEMS FOR PRACTICE|30 Videos

Similar Questions

Explore conceptually related problems

If x^2+ax+1=0 is a factor of ax^3+ bx + c , then which of the following conditions are not valid

If (x ^(2) -1) is a factor of ax ^(4) + bx ^(3) + cx ^(2) + dx +e, then show that a + c +e =b +d=0

If ( x+ 5) and ( x - 3) are the factors of ax^(2) + bx + c , then values of a,b and c are

If both (x-2) and ( x- (1)/(2)) are the factors of ax^(2) + 5x + b , then show that a =b .

If the quotient on dividing 5x^(4) + 4x^(3) + 2x + 1 by x + 3 is 5x^(3) + ax^(2) + bx - 97 then find the values of a,b and also remainder.

If int((2x+3)dx)/(x(x+1)(x+2)(x+3)+1)=C-(1)/(f(x)) where f(x) is of the form of ax^(2)+bx+c , then the value of f(1) is

If a^(2) + b^(2) = c^(2), c != 0 , then find the non-zero solution of the equation: sin^(-1).(ax)/(c) + sin^(-1).(bx)/(c) = sin^(-1) x

If the function f(x) = axe^(bx^(2)) has maximum value at x=2 such that f(2) =1 , then find the values of a and b

PREMIERS PUBLISHERS-THEORY OF EQUATIONS-Problems for practice (Choose the correct answer )
  1. The number of solution of x^2+|x+1|=1 is :

    Text Solution

    |

  2. If alpha, beta , gamma are the roots of the equation x^3-3x+2=0 then ...

    Text Solution

    |

  3. The sum of square of roots of the equation 2x^4+x^2+x+2=0 is :

    Text Solution

    |

  4. If alpha , beta, gamma are the roots of the equation x^3-4x^2+3x-1=0,...

    Text Solution

    |

  5. Form a polynomial equation with integer coefficients with sqrt((sqrt2)...

    Text Solution

    |

  6. A straight line and parabola cannot intersect at more than points.

    Text Solution

    |

  7. If a,b,c are rational , the roots of equation x^2-2ax+(a^2-b^2+2bc-c^...

    Text Solution

    |

  8. If x^(2) + ax + 1 is a factor of ax^(3) + bx + c, them find the condi...

    Text Solution

    |

  9. According to the rational root equation which number is not possible ...

    Text Solution

    |

  10. P(x)=x^5-4x^3+2x^2+x+7 cannot have more than positive real root.

    Text Solution

    |

  11. The value of k for which the equation x^2+kx+25=0 has equal roots is

    Text Solution

    |

  12. If alphabetagamma are the roots of x^3-3x^2+4x+1=0 then sum1/(alphabet...

    Text Solution

    |

  13. The only real root of x^3+2x^2+2x+1=0 is

    Text Solution

    |

  14. Find the correct statement for the following :

    Text Solution

    |

  15. Find the incorrect statement for the following :

    Text Solution

    |

  16. Identify the correct pair from the following statements: (i)For an ...

    Text Solution

    |

  17. Find the odd one out : If sqrtp+sqrtq is a root of a polynomial eq...

    Text Solution

    |

  18. Assertion: The polynomial 5x^9+3x^5-x^4-2x^2+5 has atleast six imagina...

    Text Solution

    |

  19. Find the odd one out : Given x^3-5x^2+6x=0

    Text Solution

    |

  20. If x^2+2(k+2)x+9k=0 has equal roots then k is :

    Text Solution

    |