Home
Class 11
MATHS
If a ,b ,c be the sides of A B C and eq...

If `a ,b ,c` be the sides of ` A B C` and equations `a x^2+b x+c=0` and `5x^2+12x+13=0` have a common root, then find `/_Cdot`

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 a ,b ,c in R and equations a x^2+b x+c=0 and x^2+2x+3=0 have a common root, then find a : b : c

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

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

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+2x+3=0 and ax^2+bx+c=0 , a, b, c in R, have a common root, then a:b:c is

If the equations x^2+ax+b=0 and x^2+bx+a=0 have one common root. Then find the numerical value of a+b.

If the equations a x^2+b x+c=0 and x^3+3x^2+3x+2=0 have two common roots, then a) a=b=c b) a=b!=c c) a=-b=c d) a+b+c=3

If the quadratic equations x^2+ax+b=0 and x^2+bx+a=0(aneb) have a common root , find the numerical value of (a+b).

Find the condition on a , b ,c ,d such that equations 2a x^3+bx^2+c x+d=0 and 2ax^2+3b x+4c=0 have a common root.

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.

CENGAGE PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. Find the minimum value of |z-1| if ||z-3|-|z+1||=2.

    Text Solution

    |

  2. If x=omega-omega^2-2 then , the value of x^4+3x^3+2x^2-11x-6 is (where...

    Text Solution

    |

  3. If a ,b ,c be the sides of A B C and equations a x^2+b x+c=0 and 5x^2...

    Text Solution

    |

  4. Find the greatest and the least value of |z1+z2| ifz1=24+7i and |z2|=6...

    Text Solution

    |

  5. If the complex numbers x and y satisfy x^3-y^3=98 ia n dx-y=7i ,t h e ...

    Text Solution

    |

  6. If b^2<2a c , then prove that a x^3+b x^2+c x+d=0 has exactly one real...

    Text Solution

    |

  7. If z is any complex number such that |z+4|lt=3, then find the greatest...

    Text Solution

    |

  8. If z1, z2 and z3, are the vertices of an equilateral triangle ABC suc...

    Text Solution

    |

  9. If two roots of x^3-a x^2+b x-c=0 are equal in magnitude but opposite ...

    Text Solution

    |

  10. For any complex number z find the minimum value of |z|+|z-2i|

    Text Solution

    |

  11. The greatest positive argument of complex number satisfying |z-4|=R e(...

    Text Solution

    |

  12. If alpha,betaa n dgamma are the roots of x^3+8=0 then find the equat...

    Text Solution

    |

  13. Prove that the distance of the roots of the equation |sintheta1|z^3+|s...

    Text Solution

    |

  14. Let z1a n dz2 be two distinct complex numbers and let z=(1-t)z1+t z2 f...

    Text Solution

    |

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

    Text Solution

    |

  16. If |z1-1|lt=1,|z2-2|lt=2,|z(3)-3|lt=3, then find the greatest value o...

    Text Solution

    |

  17. If the roots of equation x^3+a x^2+b=0a r ealpha1,alpha2 and alpha3(a ...

    Text Solution

    |

  18. If z is a complex number, then find the minimum value of |z|+|z-1|+|2z...

    Text Solution

    |

  19. Let |z|=2and w=(z+1)/(z-1),where z ,w , in C (where C is the set of c...

    Text Solution

    |

  20. If alpha,betaa n dgamma are roots of 7x^3-x-2=0 , then find the value ...

    Text Solution

    |