Home
Class 12
MATHS
lf the quadratic equations x^2+bx+c=0 a...

lf the quadratic equations `x^2+bx+c=0` and `bx^2+cx+1=0` have a common root then prove that either `b+c+1=0` or `b^2+c^2+1=bc+b+c`.

Promotional Banner

Topper's Solved these Questions

  • QUADRATIC EQUATION

    MOTION|Exercise EXERCISE 4 (PREVIOUS YEAR| JEE MAIN)|25 Videos

  • QUADRATIC EQUATION

    MOTION|Exercise EXERCISE -2 (MCQ)|9 Videos

  • PERMUTATION AND COMBINATION

    MOTION|Exercise EXAMPLE|23 Videos

  • SEQUENCE & SERIES

    MOTION|Exercise Exercise -4 Level -II Previous Year /JEE Advanced|22 Videos

Similar Questions

Explore conceptually related problems

If the quadratic equations x^(2)+bx+c=0 and bx^(2)+cx+1=0 have a common root then prove that either b+c+1=0 or b^(2)+c^(2)+1=bc+b+c

If the equations ax^(2)+bx+C=0 and x^(2)+2x+4=0 have a common root then find a:b:c

If a,b,c in R and the equation ax^(2)+bx+c=0 and x^(2)+x+1=0 have a common root,then

If the equation ax^(2) + bx + c = 0 and 2x^(2) + 3x + 4 = 0 have a common root, then a : b : c

If the quadratic equation ax^(2)+2cx+b=0 and ax^(2)+2bx+c=0(b!=c) have a common root,then a+4b+4c=

If the equation x^(2)+2x+3=0 and ax^(2)+bx+c=0 have a common root then a:b:c is

If the equation ax^(2)+2bx+c=0 and ax62+2cx+b=0b!=c have a common root,then (a)/(b+c)=

If x^(2)+ax+bc=0 and x^(2)+bx+ca=0 have a common root,then a+b+c=1

If the equations ax^(2)+bx+c=0 and x^(2)+x+1=0 has one common root then a:b:c is equal to

MOTION-QUADRATIC EQUATION-EXERCISE -3 (SUBJECTIVE)
  1. Show that the roots of the equation (a^(2)-bc)x^(2)+2(b^(2)-ac)x+c^(2)...

    Text Solution

    |

  2. If a x^2+b x+c=0a n db x^2+c x+a=0 have a common root and a, b, and c ...

    Text Solution

    |

  3. lf the quadratic equations x^2+bx+c=0 and bx^2+cx+1=0 have a common r...

    Text Solution

    |

  4. If the quadratic equations x^2+bx+ca=0 & x^2+cx+ab=0 (where a!= 0) ha...

    Text Solution

    |

  5. Solve the equation x^4 + 4x^3 + 5x^2 + 2x-2=0, one root being -1+sqrt...

    Text Solution

    |

  6. If alpha, beta, gamma are the roots of the equation x^3 + px^2 + qx + ...

    Text Solution

    |

  7. If alpha,betaa n dgamma are roots of 2x 63+x^3-7=0 , then find the val...

    Text Solution

    |

  8. Let alpha+ibeta,alpha, beta epsilon R, be a root of the equation x^(3)...

    Text Solution

    |

  9. Let alpha,beta,gamma are the roots of the cubic x^3-3x^2+1=0 .Find a c...

    Text Solution

    |

  10. Two roots of a biquadratic x^4-18x^3+ kx^2+ 200x-1984=0 have their pro...

    Text Solution

    |

  11. Suppose a cubic polynomial f(x) = x^3 + px^2 + qx + 72 is divisible by...

    Text Solution

    |

  12. If g(x)=x^(3)+px^(2)+qx+r where p,q,r are integers. If g(0) and g(-1)...

    Text Solution

    |

  13. If x be real then find the range of the following rational expressions...

    Text Solution

    |

  14. Find the values of k for which |(x^2+k x+1)/(x^2+x+1)|<2,AAx in R

    Text Solution

    |

  15. Find the range of values of a, such that f(x)=(ax^2+2(a+1)x+9a+4)/(x^2...

    Text Solution

    |

  16. The least value of the quadratic polynomial, f(x) = (2p^(2) + 1) x^(2)...

    Text Solution

    |

  17. Find all real numbers x such that (x-1/x)^(1/2)+(1-1/x)^(1/2)=x

    Text Solution

    |

  18. The minimum value of ((x+1/x)^6-(x^6+1/(x^6))- 2)/((x+1/x)^3+x^3+1/x^...

    Text Solution

    |

  19. Find the product of the real roots of the equation, x^2+18x +30=2sqrt(...

    Text Solution

    |

  20. The values of b for which the equation 2log(1/25)(bx+28)=1log5(12-4x-x...

    Text Solution

    |