Home
Class 9
MATHS
If the polynomial (a^(2)-b^(2))x^(2)+2ab...

If the polynomial `(a^(2)-b^(2))x^(2)+2abx+(a^(2)+b^(2))a,b,c` are constants, be a linear polynomial, then prove that a = b.

Promotional Banner

Topper's Solved these Questions

  • POLYNOMIALS

    CALCUTTA BOOK HOUSE|Exercise EXERCISE-1.2|45 Videos

  • POLYNOMIALS

    CALCUTTA BOOK HOUSE|Exercise EXERCISE-1.3|36 Videos

  • POLYNOMIALS

    CALCUTTA BOOK HOUSE|Exercise EXERCISE-1.4|52 Videos

  • LOGARITHM

    CALCUTTA BOOK HOUSE|Exercise Exercise - 7 (Long-answer type questions)|49 Videos

  • PROBABILITY

    CALCUTTA BOOK HOUSE|Exercise EXERCISE - 2|16 Videos

Similar Questions

Explore conceptually related problems

If the polynomial (a^(2)+b^(2)+c^(2)-ab-bc-ca)x^(2)+2abcx+(a^(2)+b^(2)+c^(2)) , where a, b, c are constants, be a linear polynomial, then prove that a = b = c.

If the simultaneous linear equations in two variables a^(2)x+b^(2)y=1 " and " x/(a^(2)+1)+y/(b^(2)+1)=k , where a ne b and a, b, k are constants have no solution, then prove that a^(2)+b^(2)+1=0 .

If (b^(2) + c^(2) - a^(2))/(2bc), (c^(2) + a^(2) - b^(2))/(2ca), (a^(2) + b^(2) - c^(2))/(2ab) are in A.P. and a+b+c = 0 then prove that a(b+c-a), b(c+a-b), c(a+b-c) are in A.P.

It the zeroes of the polynomial x^(3)-3x^(2)+x+1 are a-b,a,a+b find a and b.

If a,b and c are constant of motion and s = at^(2)+bt+ c , then prove that 4a(s-c) = v^(2) - b^(2) .

Determine the values of a and b when the polynomial (ax^(3)+bx^(2)+x-6) is divided by (x - 2), the remainder is 4 and (x + 2) is a factor of the polynomial.

If b/(a+b) = (a+c-b)/(b+c-a) = (a+b+c)/(2a+b+2c)("where " a + b + c ne 0) , then prove that a/2 = b/3 = c/4 .

If a, b, c are in GP then prove that, (a+2b+2c)(a-2b+2c)= a^2+ 4c^2

If the polynomial (ax^(3)+bx^(2)-x+6) be divided by (x + 2), the remainder is (-3) and if (x - 1) is a factor of this polynomial, then find the values of a and b.

If (x^(2)-2) be a factor of the polynomial (ax^(3)-bx^(2)-4) , find the values of a and b.

CALCUTTA BOOK HOUSE-POLYNOMIALS-EXERCISE-1.1
  1. Determine the co-efficients according to the directions given of the f...

    Text Solution

    |

  2. Determine the degrees of the following polynomials : x^(m)-1

    Text Solution

    |

  3. Determine the degrees of the following polynomials : (x^(p)-1)/(x-1)

    Text Solution

    |

  4. Determine the degrees of the following polynomials : (x^(4)+x^(2)y^(...

    Text Solution

    |

  5. Determine the degrees of the following polynomials : (7u^(2)-29)/(sq...

    Text Solution

    |

  6. Determine which of the following polynomials are linear, quadratic and...

    Text Solution

    |

  7. Determine which of the following polynomials are linear, quadratic and...

    Text Solution

    |

  8. Determine which of the following polynomials are linear, quadratic and...

    Text Solution

    |

  9. Determine which of the following polynomials are linear, quadratic and...

    Text Solution

    |

  10. Determine which of the following polynomials are linear, quadratic and...

    Text Solution

    |

  11. Determine which of the following polynomials are linear, quadratic and...

    Text Solution

    |

  12. Give two examples of each of the following cases : (i) (a) Monomials...

    Text Solution

    |

  13. Determine the degrees and the number of terms of each of the following...

    Text Solution

    |

  14. Determine the degrees and the number of terms of each of the following...

    Text Solution

    |

  15. Determine the degrees and the number of terms of each of the following...

    Text Solution

    |

  16. Determine the degrees and the number of terms of each of the following...

    Text Solution

    |

  17. For what value of a, the polynomial (a - 1) x + 10 will reduce to a co...

    Text Solution

    |

  18. If the expression (k^(2)-2k+1)y+sqrt17 be a constant polynomial, then ...

    Text Solution

    |

  19. If the polynomial (a^(2)-b^(2))x^(2)+2abx+(a^(2)+b^(2))a,b,c are const...

    Text Solution

    |

  20. If the polynomial (a^(2)+b^(2)+c^(2)-ab-bc-ca)x^(2)+2abcx+(a^(2)+b^(...

    Text Solution

    |