Home
Class 12
MATHS
If 2+3i is one of the roots of the equat...

If `2+3i` is one of the roots of the equation `2x^3-9x^2 + kx-13 = 0, k epsilon R,` then the real root of this equation

A

exists and is equal to `-1/2`

B

exists and is equal to `1/2`

C

exists and is equal to 1

D

does not exist

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    DISHA PUBLICATION|Exercise Exercise-1: Concept Builder (Topic -1)|15 Videos

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    DISHA PUBLICATION|Exercise Exercise-1: Concept Builder (Topic -2)|10 Videos

  • CHAPTERWISE NUMERIC INTEGER ANSWER QUESTIONS

    DISHA PUBLICATION|Exercise CHAPTER 27|15 Videos

  • CONIC SECTIONS

    DISHA PUBLICATION|Exercise Exercise-2 : Concept Applicator|30 Videos

Similar Questions

Explore conceptually related problems

If 2+3i is one of the roots of the equation 2x^(3)-9x^(2)+kx-13=0,k varepsilon R, then the real root of this equation

The root of the equation 3^(2x)-10.3^(x)+9=0 are

The number of real roots of the equation x^2-3 modx +2=0 is

If the product of the roots of the equation x^(2) - 2sqrt(2) kx + 2e^(2 log k) -1 = 0 is 31, then the roots of the equation are real for k equal to

If the product of the roots of the equation x^(2)-3kx+2e^(2ln k)-1=0 is 7 then the roots of the equation are real for k equal to

The number of real roots of the equation |x|^(2) -3|x| + 2 = 0 , is

If x=4 is one of the roots of the quadratic equation 3x^(2)+kx-2=0 , find the value of k.

Let a, b be the roots of the equation x^2 - kx + k = 0 , k in R . If a^2 + b^2 is the minimum then find the roots of the equation.

DISHA PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS -Exercise -2 : Concept Applicator
  1. If 2+3i is one of the roots of the equation 2x^3-9x^2 + kx-13 = 0, k e...

    Text Solution

    |

  2. If z1=sqrt2 (cospi/4+isin(pi/4)) and z2=sqrt3(cospi/3+isin(pi/3)) then...

    Text Solution

    |

  3. If x+iy=3/(2+costheta +i sin theta), then show that x^2+y^2=4x-3

    Text Solution

    |

  4. Write the complex number z = (i-1)/(cos pi/3 + i sin pi/3)in polar fo...

    Text Solution

    |

  5. A variable complex number z=x+iy is such that arg(z-1)/(z+1)= pi/2. S...

    Text Solution

    |

  6. If arg(z) lt 0, then find arg(-z) -arg(z).

    Text Solution

    |

  7. If f(z)=(7-z)/(1-z^2) , where z=1+2i , then |f(z)| is (|z|)/2 (b) |z| ...

    Text Solution

    |

  8. If z=x+i y, z^(1/3)=a-i b " and " x/a-y/b=lambda(a^2-b^2), then lambda...

    Text Solution

    |

  9. Amplitude of (1+sqrt3i)/(sqrt3+1)is

    Text Solution

    |

  10. If z=(3-i)/(2+i)+(3+i)/(2-i) then value of arg (zi) is

    Text Solution

    |

  11. If (y^2-5y+3)(x 62+x+1)<2x for all x in R , then fin the interval in ...

    Text Solution

    |

  12. Let x+1/x=1 and a, b and c are distict positive integer such that (x^(...

    Text Solution

    |

  13. If z=(3+7i)(a+ib), where a, b in Z-{0}, is purely imaginery, then mini...

    Text Solution

    |

  14. The value of lambda for which the sum of squares of roots of the equat...

    Text Solution

    |

  15. The set of all real numbers x for which x^2-|x+2| +x gt 0 is

    Text Solution

    |

  16. If alpha,beta are the roots of the equation ax^2+ bx +c =0, then alp...

    Text Solution

    |

  17. If log(1/2) ((x^2+6x+9)/(2(x+1)) )< - log2(x+1) then complete set of v...

    Text Solution

    |

  18. Solve: x^(2) + 2 = 0

    Text Solution

    |

  19. If a<b<c<d , then the roots of the equation (x-a)(x-c)+2(x-b)(x-d)=0 a...

    Text Solution

    |

  20. If the cube roots of unity are 1,w w^2,then the roots of the equation ...

    Text Solution

    |

  21. Find t values of the parameter a such that the rots alpha,beta of the ...

    Text Solution

    |