Home
Class 11
MATHS
If x^2+p x+1 is a factor of the expressi...

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

Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CENGAGE PUBLICATION|Exercise All Questions|363 Videos
  • CONIC SECTIONS

    CENGAGE PUBLICATION|Exercise All Questions|1167 Videos

Similar Questions

Explore conceptually related problems

If a!=0 and the line 2b x+3c y+4d=0 passes through the points of intersection of the parabolas y^2=4a x and x^2=4a y , then (a) d^2+(2b+3c)^2=0 (b) d^2+(3b+2c)^2=0 (c) d^2+(2b-3c)^2=0 (d)none of these

If the expression x^2+2(a+b+c)x+3(b c+ca+a b) is a perfect square, then a. a=b=c b. a=+-b=+-c c. a=b!=c d. none of these

If both roots of the equation a x^2+x+c-a=0 are imaginary and c > -1, then a) 3a >2+4c b) 3a<2+4c c) c < a d) none of these

If the equation |x^2+b x+c|=k has four real roots, then a. b^2-4c > 0 and 0 0 and k > (4c-b^2)/4 d. none of these

a ,b ,c x in R^+ such that a ,b ,and c are in A.P. and b ,c and d are in H.P., then a b=c d b. a c=b d c. b c=a d d. none of these

If the ratio of the roots of a x ^2+2b x+c=0 is same as the ratio of roots of p x^2+2q x+r=0, then a. (2b)/(a c)=(q^2)/(p r) b. b/(a c)=(q^2)/(p r) c. (b^2)/(a c)=(q^2)/(p r) d. none of these

If the equation a x^2+b x+c=0,a ,b ,c , in R have none-real roots, then c(a-b+c)>0 b. c(a+b+c)>0 c. c(4a-2b+c)>0 d. none of these

Given that a ,b ,c are distinct real numbers such that expressions a x^2+b x+c ,b x^2+c x+a and,c x^2+a x+b are always non-negative. Prove that the quantity (a^2+b^2+c^2)/(a b+b c+c a) can never lie in (-oo,1) uu [4 , oo) .

If a ,b , a n dc are in G.P. and x ,y , respectively, are the arithmetic means between a ,b ,a n db ,c , then the value of a/x+c/y is 1 b. 2 c. 1//2 d. none of these

Let f(x)=ax^2-bx+c^2, b != 0 and f(x) != 0 for all x ∈ R . Then (a) a+c^2 2b (c) a-3b+c^2 < 0 (d) none of these

CENGAGE PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. If z(1) and z(2) are conjugate to each other , find the principal argu...

    Text Solution

    |

  2. If a is a complex number such that |a|=1, then find the value of a, s...

    Text Solution

    |

  3. If x^2+p x+1 is a factor of the expression a x^3+b x+c , then a^2-c^2=...

    Text Solution

    |

  4. Find the value of expression (cos(pi/2)+i sin(pi/2))(cos(pi/(2^2))+i s...

    Text Solution

    |

  5. If alpha, beta are the roots of x^(2) - px + q = 0 and alpha', beta' a...

    Text Solution

    |

  6. If a ,b are complex numbers and one of the roots of the equation x^2+a...

    Text Solution

    |

  7. If |z1|=|z2|=1, then prove that |z1+z2|= |1/z1+1/z2∣

    Text Solution

    |

  8. For x in (0,1) , prove that i^(2i+3) ln((i^3x^2+2x+i)/(i x^2+2x+i^3))=...

    Text Solution

    |

  9. The sum of the non-real root of (x^2+x-2)(x^2+x-3)=12 is a.-1 b....

    Text Solution

    |

  10. If n is a positive integer, prove that |I m(z^n)|lt=n|I m(z)||z|^(n-1....

    Text Solution

    |

  11. The number of roots of the equation sqrt(x-2)(x^2-4x+3)=0 is (A) Th...

    Text Solution

    |

  12. If z1,z2 and z3,z4 are two pairs of conjugate complex numbers, then ar...

    Text Solution

    |

  13. If x=1+i is a root of the equation x^3-i x+1-i=0, then the other real ...

    Text Solution

    |

  14. Find the modulus, argument, and the principal argument of the complex ...

    Text Solution

    |

  15. Find the principal argument of the complex number ((1+i)^5(1+sqrt(3i))...

    Text Solution

    |

  16. If the expression x^2+2(a+b+c)x+3(b c+ca+a b) is a perfect square, the...

    Text Solution

    |

  17. Find the point of intersection of the curves a r g(z-3i)=(3pi)/4 and a...

    Text Solution

    |

  18. The curve y=(lambda+1)x^2+2 intersects the curve y=lambdax+3 in exactl...

    Text Solution

    |

  19. if z and w are two non-zero complex numbers such that absz=absw and ar...

    Text Solution

    |

  20. The number of irrational roots of the equation (4x)/(x^2+x+3)+(5x)/(x...

    Text Solution

    |