Home
Class 12
MATHS
If one of the factors of ax^(2)+bx+c and...

If one of the factors of `ax^(2)+bx+c` and `bx^(2)+cx+a` is common then

A

`a=0`

B

`a^(3)+b^(3)+c^(3)=3abc`

C

`a=0` or `a^(3)+b^(3)+c^(3)=3abc`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • QUADRATIC EQUATION

    MOTION|Exercise EXERCISE -2 (MCQ)|9 Videos
  • QUADRATIC EQUATION

    MOTION|Exercise EXERCISE -3 (SUBJECTIVE)|36 Videos
  • QUADRATIC EQUATION

    MOTION|Exercise EXERCISE -1 (OBJECTIVE PROBLEMS)|30 Videos
  • PERMUTATION AND COMBINATION

    MOTION|Exercise EXAMPLE|23 Videos
  • SEQUENCE & SERIES

    MOTION|Exercise Exercise -4 Level -II Previous Year /JEE Advanced|22 Videos

Similar Questions

Explore conceptually related problems

If one root of the equations ax^(2)+bx+c=0 and bx^(2)+cx+a=0, (a, b, c in R) is common, then the value of ((a^(3)+b^(3)+c^(3))/(abc))^(3) is

If the equations ax^(2) +2bx +c = 0 and Ax^(2) +2Bx+C=0 have a common root and a,b,c are in G.P prove that a/A , b/B, c/C are in H.P

If a, b, c are positive real numbers such that the equations ax^(2) + bx + c = 0 and bx^(2) + cx + a = 0 , have a common root, then

If (x + 2) is a common factor of x^(2) + ax + b and x^(2) + bx + a , then the ratio a : b is equal to

The equations ax^(2)+bx+c=0 and cx^(2)+bx+a=0 have a common root and the difference of their other roots is one. Then show that |ac|=|a^(2)-c^(2)| . Hence or otherwise find the maximum and minimum value of |(a)/( c )| .

If (x+1)and(x-1) are the factors of ax^(3)+bx^(2)+cx+d , then which of the following is true?

If x-1 is a common factor of x^(2)+ax+3 and x^(2)-bx+2 then find the value of b-a

if each pair of the equation x^(2)+ax+b=0,x^(2)+bx+c=0 and x^(2)+cx+a=0 has common root,then product of all common root is

MOTION-QUADRATIC EQUATION-EXERCISE -2 (OBJECTIVE PROBLEMS)
  1. If one root of the equation x^2+ px+ 12=0 is 4, while the equation x^...

    Text Solution

    |

  2. If roots of the equation ax^(2)+2(a+b)x+(a+2b+c)=0 are imaginary then ...

    Text Solution

    |

  3. Roots of the equation (a+b-c)x^(2)-2ax+(a-b+c)=0, (a,b, c, epsilonQ) a...

    Text Solution

    |

  4. If the roots of the equation 6x^2-7x + k=0 are rational then value of ...

    Text Solution

    |

  5. If coefficients of the equation ax^2 + bx + c = 0 , a!=0 are real and...

    Text Solution

    |

  6. If a ,b ,p ,q are nonzero real numbers, then how many oon roots would ...

    Text Solution

    |

  7. If one of the factors of ax^(2)+bx+c and bx^(2)+cx+a is common then

    Text Solution

    |

  8. If two roots of the equation x^3-px^2+qx-r=0 are equal in magnitude bu...

    Text Solution

    |

  9. If condition for a^(2)x^(4)+bx^(3)+cx^(2)+dx+f^(2) may be perfect squa...

    Text Solution

    |

  10. If a and b(!=0) are the roots of the equation x^2+ax+b=0 then the leas...

    Text Solution

    |

  11. If y =-2x^2-6x + 9, then (A) maximum value of y is -11 and it occur...

    Text Solution

    |

  12. Consider y=(2x)/(1+x^2), where x is real , then the range of expressi...

    Text Solution

    |

  13. The diagram shows the grap of y=ax^(2)+bx+c. Then

    Text Solution

    |

  14. All the values of m for whilch both the roots of the equation x^2-2m x...

    Text Solution

    |

  15. If both the roots of the quadratic equation x^2-2kx+k^2+k-5=0 are less...

    Text Solution

    |

  16. Let a,b,c be real if ax^(2)+bx+c=0 has two real roots alpha and beta w...

    Text Solution

    |

  17. If both roots of the quadratic equation x^(2)+x+p=0 exceed p where p e...

    Text Solution

    |

  18. for all x in R if mx^2-9mx+5m+1gt0 then m lies in the interval

    Text Solution

    |

  19. If a lt 0, then the value of x satisfying x ^(2)-2a|x-a| -3a ^(2)=0 i...

    Text Solution

    |

  20. If a^2+b^2+c^2=1 then ab+bc+ca lies in the interval

    Text Solution

    |