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

Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CENGAGE PUBLICATION|Exercise All Questions|363 Videos
  • CONIC SECTIONS

    CENGAGE PUBLICATION|Exercise All Questions|1167 Videos

Similar Questions

Explore conceptually related problems

If f(x)=ax^(2)+bx+c and f(x - 1) = f(x) + 2x + 1. then find the values of a and b.

If f(x)=ax^(2)+bx+c and f(x + 1) = f(x) + x + 1, then determine the values of a and b.

If f(x)=ax^(2)+bx+c and f(0) = 2, f(1) = 1, f(4) = 6, then find the valuse of a, b and c.

Let f(x)=x^(3) + bx^(2) +cx +d, 0 lt b^(2) lt c . Then f(x)-

Let f(x)=a x^2+bx +c a ,b ,c in R . If f(x) takes real values for real values of x and non-real values for non-real values of x , then (a) a=0 (b) b=0 (c) c=0 (d) nothing can be said about a ,b ,c .

Let f(x)=a x^2+b x+cdot Consider the following diagram. Then Fig c 0 a+b-c >0 a b c<0

Let a,b, c in R. " If " f(x)=ax^(2)+bx+c is such that a+b+c=3 and f(x+y)=f(x)+f(y)+xy, AA x,y in R, " then " sum_(n=1)^(10) f(n) is equal to

If f(x) = ax^2 + bx + c find a, b so that f(x + 1) = f(x) + x + 1 may hold identically.

Let f(x)=a x+b and g(x)=c x+d , a!=0. Assume a=1,b=2. If (fog)(x)=(gof)(x) for all x , what can you say about c and d ?

If the equations a x^2+b x+c=0 and x^3+3x^2+3x+2=0 have two common roots, then a) a=b=c b) a=b!=c c) a=-b=c d) a+b+c=3

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

    Text Solution

    |

  2. Multiply: (2+5i)(4-3i)

    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. It is given that n is an odd integer greater than 3 but n is 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. If roots of the equation x^2-10cx-11d=0 are a,b and those of x^2-10ax-...

    Text Solution

    |

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

    Text Solution

    |

  15. Coefficient of x^99 in the polynomial (x-1) (x-2)....(x-100) is

    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

    |