Home
Class 11
MATHS
If (x^2+p x+1) is a factor of (a x^3+b ...

If `(x^2+p x+1)` is a factor of `(a x^3+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

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CENGAGE ENGLISH|Exercise All Questions|365 Videos

  • CONIC SECTIONS

    CENGAGE ENGLISH|Exercise All Questions|1344 Videos

Similar Questions

Explore conceptually related problems

If x^2+p x+1 is a factor of the expression a x^3+b x+c , then a^2-c^2=a b b. a^2+c^2=-a b c. a^2-c^2=-a b d. none of these

If x^2-1 is a factor of a x^4+b x^3+c x^2+dx+e , show that a+c+e=b+d

If x^2-1 is a factor of a x^4+b x^3+c x^2+dx+e , show that a+c+e=b+d

If x^2-1 is a factor of a x^4+b x^3+c x^2+dx+e , show that a+c+e=b+d

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 :

If x-2 is a factor of x^2+3a x-2a, then a= (a) 2 (b) -2 (c) 1 (d) -1

If a ,\ b ,\ c are in proportion, then (a) a^2=b c (b) b^2=a c (c) c^2=a b (d) None of these

The area of a parallelogram formed by the lines a x+-b x+-c=0 is (a) (c^2)/((a b)) (b) (2 c^2)/((a b)) (c) (c^2)/(2a b) (d) none of these

The area of a parallelogram formed by the lines a x+-b y+-c=0 is (a) (c^2)/((a b)) (b) (2c^2)/((a b)) (c) (c^2)/(2a b) (d) none of these

CENGAGE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. Let z1, z2a n dz3 represent the vertices A ,B ,a n dC of the triangl...

    Text Solution

    |

  2. Let a, b, c be real numbers, a != 0. If alpha is a zero of a^2 x^2+bx...

    Text Solution

    |

  3. If (x^2+p x+1) is a factor of (a x^3+b x+c),t h e n a^2+c^2=-a b ...

    Text Solution

    |

  4. If |z| < sqrt(2)-1,t h e n|z^2+2zcosalpha|i s a. less than 1 b. sqr...

    Text Solution

    |

  5. On the Argand plane z1, z2a n dz3 are respectively, the vertices of an...

    Text Solution

    |

  6. If complex number z(z!=2) satisfies the equation z^2=4z+|z|^2+(16)/(|z...

    Text Solution

    |

  7. Both the roots of the equation (x-b)(x-c)+(x-a)(x-c)+(x-a)(x-b)=0 are ...

    Text Solution

    |

  8. Find the locus of the points representing the complex number z for...

    Text Solution

    |

  9. The equation x-2/(x-1)=1-2/(x-1) has a. no root b. one root c. two ...

    Text Solution

    |

  10. Identify the locus of z if bar z = bar a +(r^2)/(z-a).

    Text Solution

    |

  11. If the expression (1 + ir)^3 is of the form of s(1+ i) for some real '...

    Text Solution

    |

  12. Two towns A and B are 60 km a part. A school is to be built to serve ...

    Text Solution

    |

  13. Find the amplitude of sinalpha+i(1-cosalpha)

    Text Solution

    |

  14. Modulus of non zero complex number z satisfying barz +z=0 and |z|^2-4...

    Text Solution

    |

  15. Find the condition on a , b ,c ,d such that equations 2a x^3+bx^2+c x+...

    Text Solution

    |

  16. Let z=9+b i ,w h e r eb is nonzero real and i^2=-1. If the imaginary p...

    Text Solution

    |

  17. If z1a n dz2 are two complex numbers and c >0 , then prove that |z1+z2...

    Text Solution

    |

  18. Let f(x), g(x), and h(x) be the quadratic polynomials having positive ...

    Text Solution

    |

  19. Find the minimum value of |z-1 if ||z-3|-|z+1||=2.

    Text Solution

    |

  20. If x=omega-omega^2-2 then , the value of x^4+3x^3+2x^2-11x-6 is (where...

    Text Solution

    |