Home
Class 12
MATHS
Form a quadratic equation with real coef...

Form a quadratic equation with real coefficients whose one root is `3-2idot`

Text Solution

Verified by Experts

Since the complex roots always occur in conjugate pairs, so the other root is 3 + 2i. The sum of the roots is (3+ 2i) + 3 - 2i) = 6 . The product of the roots is `(3 + 2i) (3 - 2i) = 9-4i^(2) = 9 + 4 = 13`
Hence, the equation is
`x^(2) -Sx + P = 0`
`rArr x^(2) - 6x + 13 = 0`
Promotional Banner

Topper's Solved these Questions

  • THEORY OF EQUATIONS

    CENGAGE|Exercise Exercise 2.1|3 Videos

  • THEORY OF EQUATIONS

    CENGAGE|Exercise Exercise 2.2|5 Videos

  • THEORY OF EQUATIONS

    CENGAGE|Exercise Comprehension|12 Videos

  • STRAIGHT LINES

    CENGAGE|Exercise JEE Advanced Previous Year|4 Videos

  • THREE DIMENSIONAL GEOMETRY

    CENGAGE|Exercise Question Bank|20 Videos

Similar Questions

Explore conceptually related problems

The quadratic equation with real coefficients has one root 2i^(*)s

The quadratic equation with rational coefficients whose one root is 2-sqrt(3) is

Find the quadratic equation with rational coefficients whose one root is 1/(2+sqrt(5))

Statement -1 : There is just on quadratic equation with real coefficients, one of whose roots is 1/(3+sqrt7) and Statement -2 : In a quadratic equation with rational coefficients the irrational roots occur in pair.

Statement -1 : There is just one quadratic equation with real coefficient one of whose roots is 1/(sqrt2 +1) and Statement -2 : In a quadratic equation with rational coefficients the irrational roots are in conjugate pairs.

Find the quadratic equation with real coefficients which has (-5-i) as a root

One of the roots of a quadratic equation with real coefficients is (1)/((2-3i)) . Which of the following implications is/are true? 1. The second root of the equation will be (1)/((3-2i)) . 2. The equation has no real root. 3. The equation is 13x^(2)-4x+1=0. Which of the above is/are correct ?

The quadratic equation p(x)=0 with real coefficients has purely imaginary roots.Then the equation p(p(x))=0 has A.only purely imaginary roots B.all real roots C.two real and purely imaginary roots D.neither real nor purely imaginary roots

CENGAGE-THEORY OF EQUATIONS-Examples
  1. Find the values of m for which the expression 2x^2+m x y+3y^2-5y-2 can...

    Text Solution

    |

  2. Form a quadratic equation whose roots are -4a n d6.

    Text Solution

    |

  3. Form a quadratic equation with real coefficients whose one root is 3-2...

    Text Solution

    |

  4. If roots of the equation a x^2+b x+c=0 are alphaa n dbeta , find the e...

    Text Solution

    |

  5. If alpha,beta are the roots of lthe equation 2x 62-3x-6=0, find the eq...

    Text Solution

    |

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

    Text Solution

    |

  7. If roots of equation 3x^(2) + 5x + 1 = 0 are (sectheta(1) - tentheta(1...

    Text Solution

    |

  8. If a b+b c+c a=0, then solve a(b-2c)x^2+b(c-2a)x+c(a-2b)=0.

    Text Solution

    |

  9. If a ,b ,a n dc are in A.P. and one root of the equation a x^2+b c+c=0...

    Text Solution

    |

  10. If alpha is a root of the equation x^2+2x-1=0, then prove that 4alpha^...

    Text Solution

    |

  11. If the roots of the equadratic equation x^(2) + px + q = 0 " are " tan...

    Text Solution

    |

  12. The sum of roots of equation 1/(x+a)+1/(x+b)=1/c is zero find the prod...

    Text Solution

    |

  13. Solve the equation x^2+p x+45=0. it is given that the squared differen...

    Text Solution

    |

  14. If alpha,beta are the roots of the equation 2x^2-35+2=0 , the find the...

    Text Solution

    |

  15. Find a quadratic equation whose product of roots x1a n dx2 is equal...

    Text Solution

    |

  16. If p(q-r)x^2+q(r-p)x+r(p-q)=0 has equal roots, then prove that 2/q=1/p...

    Text Solution

    |

  17. Let alpha, beta in R. If alpha, beta^(2) are the roots of quadratic eq...

    Text Solution

    |

  18. If alpha,beta are roots of x^2+-p x+1=0a n dgamma,delta are the roots ...

    Text Solution

    |

  19. If the ratio of the roots of the equation x^2+p x+q=0 are equal to rat...

    Text Solution

    |

  20. Let n in Z and DeltaABC be a right tirangle with angle at C . If sin ...

    Text Solution

    |