Home
Class 11
MATHS
Suppose a ,b ,c in I such that the grea...

Suppose `a ,b ,c in I` such that the greatest common divisor for `x^2+a x+b` and `x^2+bx+c` is `(x+1)` and the least common multiple of `x^2+a x+b` and `x^2+b x+c` is `(x^3-4x^2+x+6)`. Then the value of `|a+b+c|` is equal to ___________.

Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CENGAGE PUBLICATION|Exercise All Questions|363 Videos

  • CONIC SECTIONS

    CENGAGE PUBLICATION|Exercise All Questions|1167 Videos

Similar Questions

Explore conceptually related problems

If intx^2dote^(-2x)dx=e^(-2x)(a x^2+b x+c)+d , then the value of |a/(b c)| is______

Suppose a ,b ,c are the roots of the cubic x^3-x^2-2=0. Then the value of a^3+b^3+c^3 is _____.

Find the condition so that the two equations a_1 x^2+b_1 x+c_1=0 and a_2 x^2+b_2 x+c_2=0 will have a common root.

If the equations x^2 + 2x + 3 = 0 and ax^2 + bx + + c = 0 have common root, then a : b : c is _____

If the equation x^2+ax+bc=0" and " x^2+bx+ca=0 have a common root, then a+b+c =

If f(x)=ax^(2)+bx+c and f(x + 1) = f(x) + x + 1, then determine the values of a and b.

Find the condition if equations ax^2+bx+c =0 and x^2+2x+3 =0 have a common root. (a,b,cinR)

In a A B C ,ifA B=x , B C=x+1,/_C=pi/3 , then the least integer value of x is

If a x^2+b x+c=0 and b x^2+c x+a=0 have a common root and a, b, and c are nonzero real numbers, then find the value of (a^3+b^3+c^3)//a b c

CENGAGE PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. If i z^4+1=0, then prove that z can take the value cospi//8+isinpi//...

    Text Solution

    |

  2. Find the value of x such that ((x+alpha)^n-(x+beta)^n)/(alpha-beta)=(s...

    Text Solution

    |

  3. Suppose a ,b ,c in I such that the greatest common divisor for x^2+a ...

    Text Solution

    |

  4. Find the value of following expression: [(1-cospi/(10)+isinpi/(10))/(1...

    Text Solution

    |

  5. Dividing f(z) by z- i, we obtain the remainder i and dividing it by z...

    Text Solution

    |

  6. If the roots of the cubic equation, x^3+a x^2+b x+c=0 are three consec...

    Text Solution

    |

  7. If z1, z2 in C ,z1^2+z2^2 in R ,z1(z1^2-3z2^2)=2 and z2(3z1^2-z2^2)...

    Text Solution

    |

  8. If cosalpha+cosbeta+cosgamma=0 a n d a l so sinalpha+sinbeta+singamm...

    Text Solution

    |

  9. If x+y+z=12 andx^2+y^2+z^2=96 and 1/x+1/y+1/z=36 , then find the valu...

    Text Solution

    |

  10. Prove that (1+i)^n+(1-i)^n=2^((n+2)/2).cos((npi)/4), where n is a pos...

    Text Solution

    |

  11. The set {R e((2i z)/(1-z^2)): z is a complex number , |z|=1,z=+-1} is...

    Text Solution

    |

  12. If the equation x^2+ax+bc=0" and " x^2+bx+ca=0 have a common root, the...

    Text Solution

    |

  13. If a r g["z"1("z"3-"z"2)]=a r g["z"3("z"2-"z"1)] , then prove that O ,...

    Text Solution

    |

  14. If x" - "i y" "=sqrt((a-i b)/(c-i d)) prove that (x^2+y^2)^2=(a^2+b^2...

    Text Solution

    |

  15. If x^3+3x^2-9x+c is of the form (x-alpha)^2(x-beta) , then c is equ...

    Text Solution

    |

  16. If x=a+b,y=a alpha+b beta and z=abeta+ b alpha , where alpha and beta...

    Text Solution

    |

  17. If z=(a+ib)^5+(b+ia)^5 then prove that Re(z)=Im(z), where a,b in R.

    Text Solution

    |

  18. If a and b are positive numbers and eah of the equations x^2+a x+2b=0 ...

    Text Solution

    |

  19. Find the real values of x and y for which the following equation is sa...

    Text Solution

    |

  20. The three angular points of a triangle are given by Z=alpha, Z=beta,Z=...

    Text Solution

    |