Home
Class 11
MATHS
If the equation |x^2+b x+c|=k has four r...

If the equation `|x^2+b x+c|=k` has four real roots, then a. `b^2-4c > 0` and `0 < k < (4c-b^2)/4` b. `b^2-4c < 0` and `0 < k < (4c-b^2)/4` c. `b^2-4c > 0` and `k > (4c-b^2)/4` 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 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

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 a x^2+b x+c=0(a >0) has two real roots alphaa n dbeta such that alphalt-2 and betagt2, then which of the following statements is/are true? (a) a-|b|+c<0 (b) clt0,b^2-4a cgt0 (c) 4a-2|b|+c<0 (d) 9a-3|b|+c<0

If the equation a x^2+b x+c=x has no real roots, then the equation a(a x^2+b x+c)^2+b(a x^2+b x+c)+c=x will have a. four real roots b. no real root c. at least two least roots d. none of these

If a x^2+b x+c=0,a ,b ,c in R has no real zeros, and if c 0 (c) a >0

If a and c are the lengths of segments of any focal chord of the parabola y^2=2b x ,(b >0), then the roots of the equation a x^2+b x+c=0 are (a) real and distinct (b) real and equal (c) imaginary (d) none of these

If a ,b ,c ,d in R , then the equation (x^2+a x-3b)(x^2-c x+b)(x^2-dx+2b)=0 has a) 6 real roots b) at least 2 real roots c) 4 real roots d) none of these

If the roots of the equation ax^2+bx+c=0 (a!=0) are reciprocal to each other then a) a=b b) a=c c) b=c d) b^2=4ac

If the equation a x^2+b x+c=0 has two positive and real roots, then prove that the equation a x^2+(b+6a)x+(c+3b)=0 has at least one positive real root.

CENGAGE PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. If the equation x^2=a x+b=0 has distinct real roots and x^2+a|x|+b=0 h...

    Text Solution

    |

  2. Given that x, y in R. Solve: x/(1+2i)+y/(3+2i)=(5+6i)/(8i-1)

    Text Solution

    |

  3. If the equation |x^2+b x+c|=k has four real roots, then a. b^2-4c > 0...

    Text Solution

    |

  4. If P(x) is a polynomial with integer coefficients such that for 4 dist...

    Text Solution

    |

  5. Let x ,y ,z ,t be real numbers x^2+y^2=9, z^2+t^2=4, and xt-y z=6 Th...

    Text Solution

    |

  6. If a ,b ,c are distinct positive numbers, then the nature of roots of ...

    Text Solution

    |

  7. If (b^2-4a c)^2(1+4a^2)<64 a^2, a<0 , then maximum value of quadratic ...

    Text Solution

    |

  8. For x^2-(a+3)|x|+4=0 to have real solutions, the range of a is a. (-oo...

    Text Solution

    |

  9. Find the number of integal values of x satisfying sqrt(-x^2+10x-16)...

    Text Solution

    |

  10. If x^(2) +ax - 3x-(a+2) = 0 has real and distinct roots, then minimum ...

    Text Solution

    |

  11. Let alpha+ibeta;alpha,beta in R , be a root of the equation x^3+q x+r...

    Text Solution

    |

  12. In equation x^4-2x^3+4x^2+6x-21=0 if two its roots are equal in magn...

    Text Solution

    |

  13. If alpha,beta,gamma are the roots of the equation x^3+p x^2+q x+r=0, t...

    Text Solution

    |

  14. The equation x^3+5x^2+px+q=0 and x^3+7x^2+px+r=0 have two roots in com...

    Text Solution

    |

  15. If alpha,beta,gamma are the roots of he euation x^3+4x+1=0, then find ...

    Text Solution

    |

  16. If the roots of the equation x^3+P x^2+Q x-19=0 are each one more that...

    Text Solution

    |

  17. If a ,b ,p ,q are non zero real numbers, then how many comman roots wo...

    Text Solution

    |

  18. If x^2+p x+q=0a n dx^2+q x+p=0,(p!=q) have a common roots, show that 1...

    Text Solution

    |

  19. a,b,c are positive real numbers forming a G.P. If ax^2+2bx+c=0and d...

    Text Solution

    |

  20. If equations x^2+a x+12=0. x^2+b x+15=0a n dx^2+(a+b)x+36=0, have a co...

    Text Solution

    |