Home
Class 12
MATHS
Let f (x) =x ^(2) + bx + c AA in R, (b,c...

Let `f (x) =x ^(2) + bx + c AA in R, (b,c, in R) ` attains its least value at `x =-` and the graph of `f (x)` cuts y-axis at `y =2.`
If `f (x) =a` has two distinct real roots, then comlete set of values of a is :

A

`(1,oo)`

B

`(-2, -1)`

C

`(0,1)`

D

`(1,2)`

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • QUADRATIC EQUATIONS

    VK JAISWAL|Exercise EXERCISE (MATCHING TYPE PROBLEMS)|3 Videos

  • QUADRATIC EQUATIONS

    VK JAISWAL|Exercise EXERCISE (SUBJECTIVE TYPE PROBLEMS)|45 Videos

  • QUADRATIC EQUATIONS

    VK JAISWAL|Exercise EXERCISE (ONE OR MORE THAN ONE ANSWER IS/ARE CORRECT)|44 Videos

  • PROBABILITY

    VK JAISWAL|Exercise Exercise -5 : Subjective Type problems|12 Videos

  • SEQUENCE AND SERIES

    VK JAISWAL|Exercise EXERCISE (SUBJECTIVE TYPE PROBLEMS)|21 Videos

Similar Questions

Explore conceptually related problems

Let f (x) =x ^(2) + bx + c AA in R, (b,c, in R) attains its least value at x =-1 and the graph of f (x) cuts y-axis at y =2. If f (x) =a has two distinct real roots, then comlete set of values of a is :

Let f(x)=x^(2)+bx+c AA x in R,(b,c in R) attains its least value at x=-1 and the graph of f(x) cuts y-axis at y=2

Let f (x) =x ^(2) + bx + c AA in R, (b,c, in R) attains its least value at x =- and the graph of f (x) cuts y-axis at y =2. The value of f (-2) + f(0) + f(1)=

Let f (x) =x ^(2) + bx + c AA in R, (b,c, in R) attains its least value at x =- and the graph of f (x) cuts y-axis at y =2. The least valur of f 9x) AA x in R is :

Let f(x)=(e^(x))/(x^(2))x in R-{0}. If f(x)=k has two distinct real roots,then the range of k, is

Let f (x) =ax ^(2) + bx+ c,a gt = and f (2-x) =f (2+x) AA x in R and f (x) =0 has 2 distinct real roots, then which of the following is true ?

Let f (x) =x ^(2) +bx+c, minimum value of f (x) is -5, then abosolute value of the difference of the roots of f (x) is :

Let R be the region in the first quadrant boounded by the x and y axis and the graphs of f(x)=(9)/(25)x+b and y=f^(-1)(x), If the area of R is 49, then the value of b, is

Let f(x)=x^(2)+ax+b. If AA x in R, there exist a real value of y such that f(y)=f(x)+y, then find themaximum value of 100a.

Let f (x) =ax ^(2) +bx + c,a ne 0, such the f (-1-x)=f (-1+ x) AA x in R. Also given that f (x) =0 has no real roots and 4a + b gt 0. Let p =b-4a, q=2a +b, then pq is:

VK JAISWAL-QUADRATIC EQUATIONS -EXERCISE (COMPREHENSION TYPE PROBLEMS)
  1. If alpha, beta the roots of equation (k + 1 )x ^(2) -(20k +14) x + 91...

    Text Solution

    |

  2. Let f (x) =x ^(2) + bx + c AA in R, (b,c, in R) attains its least val...

    Text Solution

    |

  3. Let f (x) =x ^(2) + bx + c AA in R, (b,c, in R) attains its least val...

    Text Solution

    |

  4. Let f (x) =x ^(2) + bx + c AA in R, (b,c, in R) attains its least val...

    Text Solution

    |

  5. Consider the equation log2 ^2 x- x - 4 log2 x- m^2 -2m-13=0,mepsilon R...

    Text Solution

    |

  6. Consider the equation log (2)^(2) x -4 log (2)x-m^(2) -2m -13=0, m in ...

    Text Solution

    |

  7. The equation x ^(4) -2x ^(3) + 4x -1=0 has four distinct real roots x ...

    Text Solution

    |

  8. The equation x ^(4) -2x ^(3) + 4x -1=0 has four distinct real roots x ...

    Text Solution

    |

  9. Let f(x) polynomial of degree 5 with leading coefficient unity such th...

    Text Solution

    |

  10. Let f (x) be a polynomial of degree 5 with leading coefficient unity,...

    Text Solution

    |

  11. Let f (x) be a polynomial of degree 5 with leading coefficient unity,...

    Text Solution

    |

  12. Consider the cubic equation in x , x ^(3) - x^(2) + (x- x ^(2)) sin th...

    Text Solution

    |

  13. Consider the cubic equation in x , x ^(3) - x^(2) + (x- x ^(2)) sin th...

    Text Solution

    |

  14. Let P(x) be quadratic polynomical with real coefficient such tht for a...

    Text Solution

    |

  15. Let P(x) be quadratic polynomical with real coefficient such tht for a...

    Text Solution

    |

  16. Let t be a ral number satifying 2t ^(2) -9t ^(2) + 30 -lamda =0 where ...

    Text Solution

    |

  17. Let t be a real number satifying 2t ^(3) -9t ^(2) + 30 -lamda =0 where...

    Text Solution

    |

  18. Let t be a ral number satifying 2t ^(2) -9t ^(2) + 30 -lamda =0 where ...

    Text Solution

    |

  19. Consider a quadratic expression f (x) =tx^(2) -(2t -1) x+ (5x -1) If...

    Text Solution

    |

  20. Consider a quadratic expression f (x) =tx^(2) -(2t -1) x+ (5x -1) I...

    Text Solution

    |