Home
Class 11
MATHS
If the roots of the equation x^2+2a x+b=...

If the roots of the equation `x^2+2a x+b=0` are real and distinct and they differ by at most `2m` ,then `b` lies in the interval a.`(a^2,a^2,+m^2)` b. `(a^2-m^2, a )` c. `[a^2-m^2, a^2)` 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 both the roots of the quadratic equation x^(2) - mx + 4 = 0 are real and distinct and they lie in the interval [1, 5], then m lies in the interval

If the roots of the quadratic equation x^(2)-m(2x-5)-6=0 are equal, then m=

If the roots of the quadratic equation (b-c)x^(2)+(c-a)x+(a-b)=0 are real and equal then prove that 2b=a+c.

If the roots of the quadratic equation (b-c)x^2+(c-a)x+(a-b)= 0 are equal, then prove that 2b=a+c.

The roots of the equation a(b-2c)x^(2)+b(c-2a)x+c(a-2b)=0 are, when ab+bc+ca=0

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

If roots of equation x^2-2c x+a b=0 are real and unequal, then prove that the roots of x^2-2(a+b)x+a^2+b^2+2c^2=0 will be imaginary.

All the values of m for whilch both the roots of the equation x^2-2m x+m^2-1=0 are greater than -2 but less than 4 lie in the interval A -2 B. m >3 C. -1ltmlt3 D. 1ltmlt4

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 the roots of the equation a x^2+b x+c=0 are of the form (k+1)/k and (k+2)/(k+1) ,then (a+b+c)^2 is equal to 2b^2-a c b. a 62 c. b^2-4a c d. b^2-2a c

CENGAGE PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. If alpha,beta are the roots of a x^2+c=b x , then the equation (a+c y)...

    Text Solution

    |

  2. If z=r e^(itheta) , then prove that |e^(i z)|=e^(-r sintheta)

    Text Solution

    |

  3. If the roots of the equation x^2+2a x+b=0 are real and distinct and th...

    Text Solution

    |

  4. Z1!=Z2 are two points in an Argand plane. If a|Z1|=b|Z2|, then prove t...

    Text Solution

    |

  5. If the ratio of the roots of a x ^2+2b x+c=0 is same as the ratio of r...

    Text Solution

    |

  6. Find real value of x and y for which the complex numbers -3+i x^2y ...

    Text Solution

    |

  7. Show that ((x+b)(x+c))/((b-a)(c-a))+((x+c)(x+a))/((c-b)(a-b))+((x+a)(x...

    Text Solution

    |

  8. Show that e^(2m itheta)((icottheta+1)/(i cottheta-1))^m=1.

    Text Solution

    |

  9. A certain polynomial P(x)x in R when divided by kx-a ,x-ba n dx-c lea...

    Text Solution

    |

  10. It is given that complex numbers z1 and z2 satisfy |z1|=2 and |z2|=3....

    Text Solution

    |

  11. If c ,d are the roots of the equation (x-a)(x-b)-k=0 , prove that a, b...

    Text Solution

    |

  12. If z1^2+z2^2+2z1.z2.costheta= 0 prove that the points represented by ...

    Text Solution

    |

  13. If (a^2-1)x^2+(a-1)x+a^2-4a+3=0 is identity in x , then find the val...

    Text Solution

    |

  14. Show that a real value of x will satisfy the equation (1-i x)//(1+i x)...

    Text Solution

    |

  15. Prove that the roots of the equation (a^4+b^4)x^2+4a b c dx+(c^4+d^4)=...

    Text Solution

    |

  16. If a+i b=((x+i)^2)/(2x^2+1), prove that a^2+b^2=((x^2+1)^2)/((2x^2+1)^...

    Text Solution

    |

  17. If the roots of the equation x^2-8x+a^2-6a=0 are real distinct, then f...

    Text Solution

    |

  18. Solve :z^2+|z|=0 .

    Text Solution

    |

  19. If roots of equation x^2-2c x+a b=0 are real and unequal, then prove ...

    Text Solution

    |

  20. Find the range of real number alpha for which the equation z+alpha|z-1...

    Text Solution

    |