Home
Class 11
MATHS
If set of values a for which f(x)=a x^2-...

If set of values `a` for which `f(x)=a x^2-(3+2a)x+6, a!=0` is positive for exactly three distinct negative integral values of `x` is `(c , d]` , then the value of `(c^2 + 4|d|)` is equal to ________.

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

For each positive or negative value of x and y except zero the value of x^2 + y^2 is always positive, Explain.

Set of value of k(kinR) for which equation x^2-4abs(x)+3-abs(k-1)=0 will have exactly four roots is

If the roots of the cubic equation, x^3+a x^2+b x+c=0 are three consecutive positive integers, then the value of (a^2//(b+1)) is equal to?

Find the minimum integral value of k for which the equation e^(x)=kx^(2) has exactly three real distinct solutions.

All the values of ' a ' for which the quadratic expression a x^2+(a-2)x-2 is negative for exactly two integral values of x may lie in (a) [1,3/2] (b) [3/2,2) (c) [1,2) (d) [-1,2)

Let y=f(x)=4x^(3)+2x-6 , then the value of int_(0)^(2)f(x)dx+int_(0)^(30)f^(-1)(y)dy is equal to _________.

If the inequality sin^2x+acosx+a^2>1+cosx holds for any x in R , then the largest negative integral value of a is -4 (b) -3 (c) -2 (d) -1

Number of integral values of b for which the equation (x^3)/3-x=b has three distinct solutions is____

The set of all values of x for which ((x+1)(x-3)^(2)(x-5)(x-4)^(3)(x-2))/(x) lt 0

Let f(x)=x+2|x+1|+2|x-1|dot If f(x)=k has exactly one real solution, then the value of k is (a) 3 (b) 0 (c) 1 (d) 2

CENGAGE PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. If equation x^4-(3m+2)x^2+m^2=0(m >0) has four real solutions which ar...

    Text Solution

    |

  2. Number of positive integers x for which f(x)=x^3-8x^2+20 x-13 is a pri...

    Text Solution

    |

  3. If set of values a for which f(x)=a x^2-(3+2a)x+6, a!=0 is positive fo...

    Text Solution

    |

  4. Polynomial P(x) contains only terms of odd degree. when P(x) is divide...

    Text Solution

    |

  5. If the equation 2x^2+4x y+7y^2-12 x-2y+t=0, where t is a parameter has...

    Text Solution

    |

  6. Let alpha1,beta1 be the roots x^2-6x+p=0a n d alpha2,beta2 be the root...

    Text Solution

    |

  7. If sqrt(sqrt(sqrt(x)))=(3x^4+4)^(1/64), then the value of x^4 is.

    Text Solution

    |

  8. Let P(x)=x^4+a x^3+b x^2+c x+d be a polynomial such that P(1)=1,P(2)=8...

    Text Solution

    |

  9. If the equation x ^2+2(lambda+1)x+lambda^2+lambda+7=0 has only negati...

    Text Solution

    |

  10. Given alphaa n dbeta are the roots of the quadratic equation x^2-4x+k...

    Text Solution

    |

  11. If (x^2+a x+3)/(x^2+x+a) takes all real values for possible real value...

    Text Solution

    |

  12. If cos^4theta+alpha and sin^4theta+alpha are the roots of the equation...

    Text Solution

    |

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

    Text Solution

    |

  14. If a ,b ,c in R a n d a b c<0 , then equation b c x^2+(2b+c-a)x+a...

    Text Solution

    |

  15. For the quadratic equation x^2+2(a+1)x+9a-5=0, which of the following ...

    Text Solution

    |

  16. Let P(x)=x^2+b x+cw h e r eba n dc are integer. If P(x) is a factor ...

    Text Solution

    |

  17. If |a x^2+b x+c|lt=1 for all x in [0, 1], then a.|a|lt=8 b. |b|>8 ...

    Text Solution

    |

  18. Let f(x)=a x^2+b x+cdot Consider the following diagram. Then Fig c<0...

    Text Solution

    |

  19. If roots of a x^2+b x+c=0 are alphaa n dbetaa n d4a+2b+c >0,4a -2b+c >...

    Text Solution

    |

  20. The equation (x/(x+1))^2+(x/(x-1))^2=a(a-1) has

    Text Solution

    |