Home
Class 12
MATHS
Let f (x) =ax ^(2) +bx + c,a ne 0, such ...

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:

A

negative

B

positive

C

0

D

nothing can be said

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • QUADRATIC EQUATIONS

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise EXERCISE (MATCHING TYPE PROBLEMS)|4 Videos

  • QUADRATIC EQUATIONS

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise EXERCISE (SUBJECTIVE TYPE PROBLEMS)|45 Videos

  • QUADRATIC EQUATIONS

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise EXERCISE (ONE OR MORE THAN ONE ANSWER IS/ARE CORRECT)|42 Videos

  • PROBABILITY

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise Exercise -5 : Subjective Type problems|11 Videos

  • SEQUENCE AND SERIES

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise EXERCISE (SUBJECTIVE TYPE PROBLEMS)|21 Videos

Similar Questions

Explore conceptually related problems

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 alpha =4a -2b+c, beta =9a+3b+c, gamma =9a -3b+c, then which of the following is correct ?

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) = ax^(2) - bx + c^(2), b ne 0 and f(x) ne 0 for all x in R . Then

If f(x) = ax^(2) + bx + c , where a ne 0, b ,c in R , then which of the following conditions implies that f(x) has real roots?

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

Let f(x) = a x^2 + bx + c , where a, b, c in R, a!=0 . Suppose |f(x)| leq1, x in [0,1] , then

Let f(x+(1)/(x))=x^(2)+(1)/(x^(2)),(x ne 0) then f(x) equals

Let f(x) be a continuous function such that f(0) = 1 and f(x)=f(x/7)=x/7 AA x in R, then f(42) is

Let f (x) =x ^(2)-bx+c,b is an odd positive integer. Given that f (x)=0 has two prime numbers an roots and b+c =35. If the least value of f (x) AA x in R is lamda, then |(lamda)/(3)| is equal to (where [.] denotes greatest integer functio)

If f(x) = ax^(2) + bx + c is such that |f(0)| le 1, |f(1)| le 1 and |f(-1)| le 1 , prove that |f(x)| le 5//4, AA x in [-1, 1]

VIKAS GUPTA (BLACK BOOK) ENGLISH-QUADRATIC EQUATIONS -EXERCISE (COMPREHENSION TYPE PROBLEMS)
  1. Let f (x) =ax ^(2) +bx + c,a ne 0, such the f (-1-x)=f (-1+ x) AA x in...

    Text Solution

    |

  2. Let f (x) =ax ^(2) +bx + c,a ne 0, such the f (-1-x)=f (-1+ x) AA x in...

    Text Solution

    |

  3. If alpha, beta the roots of equation (k + 1 )x ^(2) -(20k +14) x + 91...

    Text Solution

    |

  4. If alpha, beta the roots of equation (k + 1 )x ^(2) -(20k +14) x + 91...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  8. Consider the equation log2 ^2 x- 4 log2 x- m^2 -2m-13=0,m in R.Let the...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  17. Let P (x ) be a quadratic polynomial with real coefficients such that...

    Text Solution

    |

  18. Let P (x ) be a quadratic polynomial with real coefficients such that...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |