Home
Class 11
MATHS
For alt=0 , determine all real roots of ...

For `alt=0` , determine all real roots of the equation `x^2-2a|x-a|-3a^2=0`

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

For a le 0 , determine all the roots of the equation x^2-2a |x-a|-3a^2 = 0

For a gt0 , determine all the roots of the equations x^(2)-2a|x-a|-3a^(2)=0

Determine the roots of the equation x^(2)=4x .

The roots of the equation x^(2)+x-6=0 are

The sum of all real roots of the equation abs(x-2)^2+abs(x-2)-2 =0 is

Find the number of real roots of the equation (x-1)^2+(x-2)^2+(x-3)^2=0.

If the roots of the equation x^2+x+a=0 be real and unequal, then prove that the roots of the equation 2x^2-4(1+a)x+2a^2+3=0 are imaginary (a is real).

Find the roots of the quadratic equation |x^(2)|-3|x|+2=0 .

The sum of the real roots of the equation abs(x)^2+absx-6 =0 is

Draw the graph of y=x^(3)-x^(2)+x-2 and find the number of real root(s) of the equation x^(3)-x^(2)+x-2=0 . Also locate the root.

CENGAGE PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. If |z1|=1,|z2|=2,|z3|=3,a n d|9z1z2+4z1z3+z2z3|=12 , then find the va...

    Text Solution

    |

  2. Let Z1 = (8 + i)sin theta + (7 + 4i)cos theta and Z2 = (1 + 8i)sin th...

    Text Solution

    |

  3. For alt=0 , determine all real roots of the equation x^2-2a|x-a|-3a^2=...

    Text Solution

    |

  4. Let A={a in R} the equation (1+2i)x^3-2(3+i)x^2+(5-4i)x+a^2=0 has at ...

    Text Solution

    |

  5. Express the following in a+i b form: ((cosalpha+isinalpha)^4)/((sinbe...

    Text Solution

    |

  6. Find the root of equation 2x^2+10 x + 20=0.

    Text Solution

    |

  7. Suppose that z is a complex number the satisfies |z-2-2i|lt=1. The max...

    Text Solution

    |

  8. If 1//x+x=2costheta , then prove that x^n+1//x^n=2cosnthetadot

    Text Solution

    |

  9. 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 ...

    Text Solution

    |

  10. Find the roots of the equation 2x^2 - x + 1/8 = 0

    Text Solution

    |

  11. If |z +2 - i|=5 then the maximum value of |3z+9-7i| is K, then find k

    Text Solution

    |

  12. If x^2+3x+5=0a n da x^2+b x+c=0 have common root/roots and a ,b ,c in ...

    Text Solution

    |

  13. Find the minimum value of the expression E= |z|^2+ |z-3|^2 + |z- 6i|^2...

    Text Solution

    |

  14. The area bounded by the curves arg z = pi/3 and arg z = 2 pi /3 and a...

    Text Solution

    |

  15. If alpha!=betaa n dalpha^2=5alpha-3a n dbeta^2=5beta-3. find the equat...

    Text Solution

    |

  16. Express 1/(1-costheta+2isintheta) in the form x+i y .

    Text Solution

    |

  17. a ,b ,c are three complex numbers on the unit circle |z|=1, such that ...

    Text Solution

    |

  18. If alpha,beta are the roots of lthe equation 2x ^2-3x-6=0, find the eq...

    Text Solution

    |

  19. If z1, z2, z3 are distinct nonzero complex numbers and a ,b , c in R...

    Text Solution

    |

  20. If |z1|=15 and |z2-3-4i|=5,t h e n

    Text Solution

    |