Home
Class 12
MATHS
Let f(x)=a x^2+b x+c ,if f(-1)lt1,f(1)g...

Let `f(x)=a x^2+b x+c `,if `f(-1)lt1,f(1)gt-1,f(3)lt-4` and `a!=0` then

A

`a gt 0`

B

`a lt 1`

C

`a lt - 1//8`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • QUADRATIC EQUATION & EXPRESSION

    FIITJEE|Exercise ASSIGNMENT PROBLEMS (OBJECTIVE) Level - II|20 Videos
  • QUADRATIC EQUATION & EXPRESSION

    FIITJEE|Exercise COMPREHENSIONS - I|3 Videos
  • QUADRATIC EQUATION & EXPRESSION

    FIITJEE|Exercise ASSIGNMENT PROBLEMS (SUBJECTIVE) Level - II|28 Videos
  • PROGRESSION & SERIES

    FIITJEE|Exercise NUMERICAL BASED|3 Videos
  • SET, RELATION & FUNCTION

    FIITJEE|Exercise Exercise 3|8 Videos

Similar Questions

Explore conceptually related problems

Let f(x) =ax^(2) + bx + c and f(-1) lt 1, f(1) gt -1, f(3) lt -4 and a ne 0 , then

If f(x)=ax^(2)+bx+c, f(-1) gt (1)/(2), f(1) lt -1 and f(-3)lt -(1)/(2) , then

If f(x^(2) - 4x + 4) = x^(2) + 1 . Find f(1) if f(1) lt 8 .

Let f be a non-negative function defined on the interval [0,1] . If int_0^xsqrt(1-(f\'(t))^2)dt=int_0^xf(t)dt, 0lexle1 and f(0)=0 , then (A) f(1/2)lt1/2 and f(1/3)gt1/3 (B) f(1/2)gt1/2 and f(1/3)gt1/3 (C) f(1/2)lt1/2 and f(1/3)lt1/3 (D) f(1/2)gt1/2 and f(1/3)lt1/3

Let f(x)={(2x+a",",x ge -1),(bx^(2)+3",",x lt -1):} and g(x)={(x+4",",0 le x le 4),(-3x-2",",-2 lt x lt 0):} If a=2 and b=3, then the range of g(f(x)) is

Let f(x) = {{:( x, if , x ge 1),( x^(2), if , x lt 1):} is f a continuous function ? Why ?

FIITJEE-QUADRATIC EQUATION & EXPRESSION -ASSIGNMENT PROBLEMS (OBJECTIVE) Level - I
  1. The solution of the equation 1!+2!+3!+…+x!=k^(2) where k in l are

    Text Solution

    |

  2. If the equation x^2-(2 + m)x + (m2-4m +4) = 0 has coincident roots, th...

    Text Solution

    |

  3. Let f(x)=a x^2+b x+c ,if f(-1)lt1,f(1)gt-1,f(3)lt-4 and a!=0 then

    Text Solution

    |

  4. lf p, q, r in R and the quadratic equation px^2 + qx + r = 0 has no re...

    Text Solution

    |

  5. If x^2-4x+log(1/2)a=0 does not have two distinct real roots, then maxi...

    Text Solution

    |

  6. The least value of |a| for which tan theta and cot theta are the roots...

    Text Solution

    |

  7. If the equation x^(3)-3ax^(2)+3bx-c=0 has positive and distinct roots,...

    Text Solution

    |

  8. The value of a for which exactly one root of the equation e^(a)x^(2)-e...

    Text Solution

    |

  9. If alphaa n dbeta are the roots of x^2-a(x-1)+b=0 then find the value ...

    Text Solution

    |

  10. Consider the equation x^(3)-nx+1=0, n in N, n ge 3. Then

    Text Solution

    |

  11. If sin alpha, sin beta and cos alpha are in GP, then roots of x^2 + 2x...

    Text Solution

    |

  12. If a, b in (0, 2) and the equation (2x^2+5)/2 = x - 2cos(ax + b) has a...

    Text Solution

    |

  13. Let P(x) and Q(x) be two polynomials. If f(x) = P(x^4) + xQ(x^4) is di...

    Text Solution

    |

  14. If (y^2-5y+3)(x 62+x+1)<2x for all x in R , then fin the interval in ...

    Text Solution

    |

  15. The solution of the equation |x+1|^(2)-2|x+2|-26=0 is

    Text Solution

    |

  16. If minimum value of f(x)=(x^(2)+2bx+2c^(2)) is greater than the maximu...

    Text Solution

    |

  17. The number of real solutions (x, y, z, t) of simultaneous equations 2y...

    Text Solution

    |

  18. The set of values of a for which (a - 1) x^(2) - (a + 1) x + a - 1 ...

    Text Solution

    |

  19. if for all real value of x,(4x^2+1)/(64x^2-96x.sina+5)<1/32,then a li...

    Text Solution

    |

  20. The number of real solutions of the equation sin (e^x)= 5^x+5^-x

    Text Solution

    |