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

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

A

`a + c^(2) lt b`

B

`4a + c^(2) gt 2b`

C

`9a - 3b + c^(2) lt 0`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
2
Here, `x^(2) - bx + c^(2) = 0` does not have real roots. So,
`D lt 0 rArr b^(2) - 4ac^(2) lt 0 rArr a gt 0`
Therefore, f(x) is always positive. So,
`f(2) gt 0 rArr 4a - 2b + c^(2) gt 0`
Promotional Banner

Topper's Solved these Questions

  • THEORY OF EQUATIONS

    CENGAGE|Exercise Exercise (Multiple)|38 Videos

  • THEORY OF EQUATIONS

    CENGAGE|Exercise Exercise (Comprehension)|37 Videos

  • THEORY OF EQUATIONS

    CENGAGE|Exercise Exercise 2.13|9 Videos

  • STRAIGHT LINES

    CENGAGE|Exercise JEE Advanced Previous Year|4 Videos

  • THREE DIMENSIONAL GEOMETRY

    CENGAGE|Exercise Question Bank|12 Videos

Similar Questions

Explore conceptually related problems

Let f(x)=ax^2-bx+c^2 != 0 and f(x) != 0 for all x in R. Then (a) a^2+c^2 2 (b) c (c) a-3b+c^2 < 0 (d) non of these

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

A function f:RtoR is such that f(x+y)=f(x).f(y) for all x.y inR and f(x)ne0 for all x inR . If f'(0)=2 then f'(x) is equal to

Let f(x) = xsqrt(4ax-x^(2)),(agt0) Then f(x) is

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) = ax^(2) + bx + c . Consider the following diagram .

Let f(x) = 2x + 5. If x ne 0 then find (f (x +2) - f(2))/(x)

Let f(x)=ax^(2)+bx+c , g(x)=ax^(2)+px+q , where a , b , c , q , p in R and b ne p . If their discriminants are equal and f(x)=g(x) has a root alpha , then

Let f(x)=ax^(2)+bx+c , g(x)=ax^(2)+qx+r , where a , b , c , q , r in R and a lt 0 . If alpha , beta are the roots of f(x)=0 and alpha+delta , beta+delta are the roots of g(x)=0 , then

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

CENGAGE-THEORY OF EQUATIONS-Exercise (Single)
  1. Suppose that f(x) isa quadratic expresson positive for all real xdot I...

    Text Solution

    |

  2. Let a, b, c in R with a gt 0 such that the equation ax^(2) + bcx + b^(...

    Text Solution

    |

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

    Text Solution

    |

  4. Let f(x)=a x^2+b x+a ,b ,c in Rdot If f(x) takes real values for real...

    Text Solution

    |

  5. If both roots of the equation a(x^2-1)+x+c are imaginary and c gt -1 t...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  9. If the equation a x^2+b x+c=x has no real roots, then the equation a(a...

    Text Solution

    |

  10. If ax^(2) + bx + c = 0 has imaginary roots and a - b + c gt 0 ....

    Text Solution

    |

  11. Given x, y in R , x^(2) + y^(2) gt 0 . Then the range of (x^(2) + ...

    Text Solution

    |

  12. x1a n dx2 are the roots of a x^2+b x+c=0a n dx1x2<0. Roots of x1(x-x2)...

    Text Solution

    |

  13. If a ,b ,c ,d are four consecutive terms of an increasing A.P., then t...

    Text Solution

    |

  14. If roots of x^2-(a-3)x+a=0 are such that at least one of them is great...

    Text Solution

    |

  15. All the values of m for whilch both the roots of the equation x^2-2m x...

    Text Solution

    |

  16. if the roots of the quadratic equation (4p - p^(2) - 5)x^(2)-(2p−1)x+3...

    Text Solution

    |

  17. The interval of a for which the equation t a n^2x-(a-4)tanx+4-2a=0 has...

    Text Solution

    |

  18. The range of a for which the equation x^2+ax-4=0 has its smaller root ...

    Text Solution

    |

  19. Find the set of all possible real value of a such that the inequality ...

    Text Solution

    |

  20. If the equation cof^4x-2cos e c^2x+a^2=0 has at least one solution, th...

    Text Solution

    |