Home
Class 12
MATHS
If (x^2+p x+1) is a factor of (a x 63+b ...

If `(x^2+p x+1)` is a factor of `(a x 63+b x+c),t h e n` `a^2+c^2=-a b` b. `a^2-c^2=-a b` c. `a^2-c^2=a b` d. none of these

A

`a ^(2)+ xc ^(2) =-ab`

B

`a ^(2) + c ^(2) =ab`

C

`a ^(2) - c ^(2)=ab`

D

`a ^(2) - c ^(2) =-ab`

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • QUADRATIC EQUATIONS

    VK JAISWAL|Exercise EXERCISE (ONE OR MORE THAN ONE ANSWER IS/ARE CORRECT)|44 Videos

  • QUADRATIC EQUATIONS

    VK JAISWAL|Exercise EXERCISE (COMPREHENSION TYPE PROBLEMS)|23 Videos

  • PROBABILITY

    VK JAISWAL|Exercise Exercise -5 : Subjective Type problems|12 Videos

  • SEQUENCE AND SERIES

    VK JAISWAL|Exercise EXERCISE (SUBJECTIVE TYPE PROBLEMS)|21 Videos

Similar Questions

Explore conceptually related problems

If x ^(2) +bx+b is a factor of x ^(3) +2x ^(2)+2x + c (c ne 0), then b-c is :

If x ^(2)+bx+b is a factor of x ^(3) +2x ^(2) +2x+c (c ne 0), then b-c is :

The distance of the point P(a ,\ b ,\ c) from the x-axis is a. sqrt(b^2+c^2) b. sqrt(a^2+c^2) c. sqrt(a^2+b^2) d. none of these

If f(x)=f(x)={(sin(a+1)x+sinx)/(x^x c),x<0(sqrt(x+b x^2)-sqrt(x))/(b xsqrt(x)),xgeq0,x-0 is continuous at x=0,t h e n a=-3/2,b=0,c=1/2 (b) a=-3/2,b=1,c=-1/2 a=-3/2,b in R-[0],c=1/2 (d) none of these

If x-a is a factor of x^(3)-3x^(2)a+2a^(2)x+b then the value of b is 0(b)2(c)1(d)3

If a, b, c are real and x^3-3b^2x+2c^3 is divisible by x -a and x - b, then (a) a =-b=-c (c) a = b = c or a =-2b-_ 2c (b) a = 2b = 2c (d) none of these

A\ (6,3),\ B(-3,5),\ C(4,-2)\ a n d\ D(x ,3x) are four points. If "Delta"D B C :"Delta"A B C=1:2, then x is equal to a. 11/8 b. 8/11 c. 3 d. none of these

If (x-2) is a common factor of the expressions x^(2)+ax+b and x^(2)+cx+d , then (b-d)/(c-a)

If sinalpha and cosalpha are the roots of the equation a x^2+b x+c=0 , then b^2= a^2-2a c (b) a^2+2a c (c) a^2-a c (d) a^2+a c

VK JAISWAL-QUADRATIC EQUATIONS -EXERCISE (SUBJECTIVE TYPE PROBLEMS)
  1. If (x^2+p x+1) is a factor of (a x 63+b x+c),t h e n a^2+c^2=-a b b. ...

    Text Solution

    |

  2. Let f(x) = ax^2 + bx + c where a,b,c are integers. If sin\ pi/7 * sin\...

    Text Solution

    |

  3. Let a, b, c, d be distinct integers such that the equation (x - a) (x ...

    Text Solution

    |

  4. Consider the equation (x^2 + x + 1)^2-(m-3)(x^2 + x + 1) +m=(1), wher...

    Text Solution

    |

  5. The number of positive integral values of m, m le 16 for which the equ...

    Text Solution

    |

  6. If the equatio (m^(2) -12 )x^(4) -8x ^(2)-4=0 has no real roots, then ...

    Text Solution

    |

  7. The least positive integral value of 'x' satisfying (e^x-2)(sin(x+pi/...

    Text Solution

    |

  8. The integral values of x for which x^2 +17x+71 is perfect square of a ...

    Text Solution

    |

  9. Let p(x) =x^6-x^5-x^3-x^2-x and alpha, beta, gamma, delta are the root...

    Text Solution

    |

  10. The number of real values of 'a' for which the largest value of the fu...

    Text Solution

    |

  11. The number of all values of n, (whre n is a whole number ) for which t...

    Text Solution

    |

  12. The number of negative intergral values of m for which the expression ...

    Text Solution

    |

  13. If the expression ax ^(4)+bx^(3)-x ^(2)+2x+3 has the remainder 4x +3 w...

    Text Solution

    |

  14. The smallest value of k for which both the roots of the equation x^2-8...

    Text Solution

    |

  15. If x ^(2) -3x+2 is a factor of x ^(4) -px ^(2) +q=0, then p+q=

    Text Solution

    |

  16. The expression x^2 + 2xy + ky^2 + 2x + k = 0 can be resolved into two ...

    Text Solution

    |

  17. The curvey y = (a +1) x ^(2) + 2 meets the curve y = ax +3, a ne -1 in...

    Text Solution

    |

  18. Find the number of integral vaues of 'a' for which the range of functi...

    Text Solution

    |

  19. When x ^(100) is divided by x ^(2) -3x +2, the remainder is (2 ^(k +1)...

    Text Solution

    |

  20. Let p (x) be a polynomial equation of least possible degree, with rati...

    Text Solution

    |

  21. The range of values k for which the equation 2 cos ^(4)x-sin ^(4)x +k=...

    Text Solution

    |