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 PUBLICATION|Exercise SOLVED EXAMPLES|14 Videos

  • THEORY OF EQUATIONS

    CENGAGE PUBLICATION|Exercise CONCEPT APPLICATION EXERCISE 2.1|3 Videos

  • THEORY OF EQUATIONS

    CENGAGE PUBLICATION|Exercise Multiple Correct Answer|6 Videos

  • STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise ARCHIVES (NUMERICAL VALUE TYPE)|1 Videos

  • THREE DIMENSIONAL GEOMETRY

    CENGAGE PUBLICATION|Exercise All Questions|291 Videos

Similar Questions

Explore conceptually related problems

Form a quadratic equation with rational coefficients whose one root is 3-sqrt5 .

Form a quadratic equation with rational coefficients whose one root is 4+sqrt7 .

Find a quadratic equation with rational co-efficient whose one root is 4+sqrt7

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

Find the quadratic equation with real coefficients which has 2±3i as a root (i=sqrt-1)

Find the quadratic equation with real coefficients which has 2+i as a root (i=sqrt-1) .

The quadratic equation p(x)=0 with real coefficients has purely imaginary roots. Then the equation p(p(x))=0 has

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

The quadratic equations p(x) =0 with real coefficients has purely imaginary roots. Then the equation p(p(x))=0 has

A quadratic equation with integral coefficients has two different prime numbers as its roots. If the sum of the coefficients of the equation is prime, then the sum of the roots is a. 2 b. 5 c. 7 d. 11

CENGAGE PUBLICATION-THEORY OF EQUATIONS-ILLUSTRATION
  1. If the expression 2x^(2)+mxy+3y^(2)-5y-2 can be resolved into two rati...

    Text Solution

    |

  2. Form a quadratic equation whose roots are -4 and 3.

    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 alpha and beta , find the e...

    Text Solution

    |

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

    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^2-35x+2=0 , the find th...

    Text Solution

    |

  15. Find a quadratic equation whose product of roots x1 a n d x2 is equa...

    Text Solution

    |

  16. Let alpha,beta in Rdot If alpha,beta^2 are the roots of quadratic equ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  20. Find the value of a for which one root of the quadratic equation (a^2-...

    Text Solution

    |