Home
Class 11
MATHS
If a ,b in R ,a!=0 and the quadratic eq...

If `a ,b in R ,a!=0` and the quadratic equation `a x^2-b x+1=0` has imaginary roots, then `(a+b+1)` is a. positive b. negative c. zero d. Dependent on the sign of `b`

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 2a+3b+6c=0 (a,b,cinR) , then the quadratic equation ax^2+bx+c =0 has

If a,b,c in R : a ne 0 and the quadratic equation ax^2+bx+c =0 has no real root, then show that (a+b+c)c gt 0

Let a, b, c be real numbers such that a+b+clt0 and the quadratic equation ax^(2)+bx+c=0 has imaginary roots. Then

If 2a+3b+6c=0 " "(a, b, c in R) , then the quadratic equation ax^(2)+bx+c=0 has at least one root -

If x is real and the roots of the equation a x^2+b x+c=0 are imaginary, then prove tat a^2x^2+a b x+a c is always positive.

If a ,b ,c in R and equations a x^2+b x+c=0 and x^2+2x+3=0 have a common root, then find a : b : c

If one of the roots of the quadratic equation be x^2 - (1+b)x+6 = 0 be 2, then find the other root.

If a ,b ,c in R a n d a b c<0 , then equation b c x^2+(2b+c-a)x+a=0 h a s (a). both positive roots (b). both negative roots (c). real roots (d) one positive and one negative root

If a,b,c in R and a+b+c=0, then the quadratic equation 3ax^2+2bx+c=0 has (a) at least one root in [0, 1] (b) at least one root in [1,2] (c) at least one root in [3/2, 2] (d) none of these

Prove that the quadratic equation 2(a^(2)+b^(2))x^(2)+2(a+b)x+1=0 will have no real root if aneb .

CENGAGE PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. Let f(x)=ax^2-bx+c^2, b != 0 and f(x) != 0 for all x ∈ R. Then (a) ...

    Text Solution

    |

  2. It is given that n is an odd integer greater than 3 but n is not a mul...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  11. If roots of the equation x^2-10cx-11d=0 are a,b and those of x^2-10ax-...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  19. If the equations x^2+ax+b=0 and x^2+bx+a=0 have one common root. Then ...

    Text Solution

    |

  20. Find all possible values of sqrt(i)+sqrt(-i)dot.

    Text Solution

    |