Home
Class 11
MATHS
If b1. b2=2(c1+c2) then at least one of ...

If `b_1. b_2=2(c_1+c_2)` then at least one of the equation `x^2+b_1x+c_1=0 and x^2+b_2x+c_2=0` has a) imaginary roots b) real roots c) purely imaginary roots 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 a ,b ,c ,d in R , then the equation (x^2+a x-3b)(x^2-c x+b)(x^2-dx+2b)=0 has a) 6 real roots b) at least 2 real roots c) 4 real roots d) none of these

Find the condition so that the two equations a_1 x^2+b_1 x+c_1=0 and a_2 x^2+b_2 x+c_2=0 will have a common root.

If a and c are the lengths of segments of any focal chord of the parabola y^2=2b x ,(b >0), then the roots of the equation a x^2+b x+c=0 are (a) real and distinct (b) real and equal (c) imaginary (d) none of these

if ax^2+bx+c = 0 has imaginary roots and a+c lt b then prove that 4a+c lt 2b

The quadratic equation p(x)=0 with real coefficients has purely imaginary roots. Then the equation p(p(x))=0 has A. only purely imaginary roots B. all real roots C. two real and purely imaginary roots D. neither real nor purely imaginary roots

If a, b , c in R and 3b^(2)-8ac lt 0 , then the equation ax^(4)+bx^(3)+cx^(2)+5x-7=0 has a) all real roots b) all imaginary roots c)exactly two real and two imaginary roots d) none

If the equation a x^2+b x+c=x has no real roots, then the equation a(a x^2+b x+c)^2+b(a x^2+b x+c)+c=x will have a. four real roots b. no real root c. at least two least roots d. none of these

If c lt a lt b lt d , then roots of the equation bx^(2)+(1-b(c+d)x+bcd-a=0

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 b_(1)b_(2)=2(c_(1)+c_(2))andb_(1),b_(2),c_(1),c_(2) are all real numbers, then at least one of the equations x^(2)+b_(1)x+c_(1)=0andx^(2)+b_(2)x+c_(2)=0 has

CENGAGE PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. Suppose A, B, C are defined as A=a^2b+a b^2-a^2c-a c^2 , B=b^2c+b c^2-...

    Text Solution

    |

  2. The integral value of m for which the root of the equation m x^2+(2m-1...

    Text Solution

    |

  3. If b1. b2=2(c1+c2) then at least one of the equation x^2+b1x+c1=0 and ...

    Text Solution

    |

  4. If the root of the equation (a-1)(x^2-x+1)^2=(a+1)(x^4+x^2+1) are real...

    Text Solution

    |

  5. If alpha and beta are roots of the equation a x^2+b x+c=0, then the ro...

    Text Solution

    |

  6. If a ,b ,c ,d in R , then the equation (x^2+a x-3b)(x^2-c x+b)(x^2-dx...

    Text Solution

    |

  7. Graph of y = f(x) is as shown in the following figure. Find th...

    Text Solution

    |

  8. In how many points graph of y=x^3-3x^2+5x-3 intersect the x-axis?

    Text Solution

    |

  9. The quadratic polynomial p(x) has the following properties:p(x)geq0 fo...

    Text Solution

    |

  10. If (1-p) is a root of quadratic equation x^2+p x+(1-p)=0, then find it...

    Text Solution

    |

  11. A polynomial in x of degree 3 vanishes when x=1 and x=-2 , ad has the ...

    Text Solution

    |

  12. Let f(x)=a^2+b x+c where a ,b , c in R and a!=0. It is known that f(5...

    Text Solution

    |

  13. If x=1 and x=2 are solutions of equations x^3+a x^2+b x+c=0 and a+b=1,...

    Text Solution

    |

  14. If x in R ,a n da ,b ,c are in ascending or descending order of magni...

    Text Solution

    |

  15. Prove that graphs y=2x-3 and y=x^2-x never intersect.

    Text Solution

    |

  16. Which of the following pair of graphs intersect ? (i) y = x^(2) - x ...

    Text Solution

    |

  17. If alpha and beta are the rootsof he equations x^2-a x+b=0a n dAn=alph...

    Text Solution

    |

  18. If alpha,beta be the roots x^2+px-q=0 and gamma,delta be the roots of ...

    Text Solution

    |

  19. If the equations a x^2+b x+c=0 and x^3+3x^2+3x+2=0 have two common roo...

    Text Solution

    |

  20. The value m for which one of the roots of x^2-3x+2m=0 is double of one...

    Text Solution

    |