Home
Class 11
MATHS
Let f(x)=ax^2-bx+c^2, b != 0 and f(x) !...

Let `f(x)=ax^2-bx+c^2, b != 0` and `f(x) != 0` for all `x ∈ R`. Then (a) `a+c^2 < b` (b) `4a+c^2 > 2b` (c) `a-3b+c^2 < 0` (d) none of these

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CENGAGE ENGLISH|Exercise All Questions|365 Videos
  • CONIC SECTIONS

    CENGAGE ENGLISH|Exercise All Questions|1344 Videos

Similar Questions

Explore conceptually related problems

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 satisfies the identity f(x+1) -f(x)= 8x+ 3 for all x in R Then (a,b)=

Let f(x)=x^3-6x^2+15 x+3 . Then, (a) f(x)>0 for all x in R (b) f(x)>f(x+1) for all x in R (c) f(x) is invertible (d) f(x)<0 for all x in R

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 varphi(x)=f(x)+f(2a-x) and f"(x)>0 for all x in [0,\ a] . Then, varphi(x) (a) increases on [0,\ a] (b) decreases on [0,\ a] (c) increases on [-a ,\ 0] (d) decreases on [a ,\ 2a]

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:

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, b, c, in R and equation f(x) - x = 0 has imaginary roots alpha, beta . If r, s be the roots of f(f(x)) - x = 0 , then |(2,alpha,delta),(beta,0,alpha),(gamma,beta,1)| is

For f(x)=x^(3)+bx^(2)+cx+d , if b^(2) gt 4c gt 0 and b, c, d in R , then f(x)

Let f:[0,5] -> [0,5) be an invertible function defined by f(x) = ax^2 + bx + C, where a, b, c in R, abc != 0, then one of the root of the equation cx^2 + bx + a = 0 is:

CENGAGE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. Suppose that f(x) is a quadratic expresson positive for all real xdot ...

    Text Solution

    |

  2. about to only mathematics

    Text Solution

    |

  3. Let f(x)=ax^2-bx+c^2, b != 0 and f(x) != 0 for all x ∈ R. Then (a) ...

    Text Solution

    |

  4. If n is n odd integer that is greater than or equal to 3 but not a mul...

    Text Solution

    |

  5. If a ,b in R ,a!=0 and the quadratic equation a x^2-b x+1=0 has imagi...

    Text Solution

    |

  6. Find the complex number omega satisfying the equation z^3=8i and lyi...

    Text Solution

    |

  7. If the expression [m x-1+(1//x)] is non-negative for all positive real...

    Text Solution

    |

  8. When the polynomial 5x^3+M x+N is divided by x^2+x+1, the remainder is...

    Text Solution

    |

  9. x1 and x2 are the roots of a x^2+b x+c=0 and x1x2<0. Roots of x1(x-x2)...

    Text Solution

    |

  10. ifomegaa n domega^2 are the nonreal cube roots of unity and [1//(a+ome...

    Text Solution

    |

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

    Text Solution

    |

  12. Find the relation if z1, z2, z3, z4 are the affixes of the vertices of...

    Text Solution

    |

  13. Let a and b are the roots of the equation x^2-10 xc -11d =0 and those...

    Text Solution

    |

  14. If z1, z2, z3 are three nonzero complex numbers such that z3=(1-lambda...

    Text Solution

    |

  15. Fill in the blanks The coefficient of x^(99) in the polynomial (x-1)...

    Text Solution

    |

  16. Let z1, z2, z3 be three complex numbers and a ,b ,c be real numbers no...

    Text Solution

    |

  17. Fill in the blanks If 2+isqrt(3) is a root of the equation x^2+p x+q=0...

    Text Solution

    |

  18. Prove that the triangle formed by the points 1,(1+i)/(sqrt(2)),a n di ...

    Text Solution

    |

  19. Fill in the blanks. If the product of the roots of the equation x^2-3k...

    Text Solution

    |

  20. Solve for z : z^2-(3-2i)z=(5i-5)dot

    Text Solution

    |