Home
Class 11
MATHS
The equation a x^2+b x+c=0 has real and...

The equation `a x^2+b x+c=0` has real and positive roots. Prove that the roots of the equation `a^2x^2+a(3b-2c)x+(2b-c)(b-c)+a c=0` re real and positive.

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

The roots of the equation (b-c) x^2 +(c-a)x+(a-b)=0 are

If a lt c lt b then the roots of the equation (a−b)x^2 +2(a+b−2c)x+1=0 are

If the roots of the equation (b-c)x^2+(c-a)x+(a-b)=0 are equal, then prove that 2b=a+c .

If the roots of the equation (b-c)x^2+(c-a)x+(a-b)=0 are equal, then prove that 2b=a+c

The roots of the equation a(b-2c)x^(2)+b(c-2a)x+c(a-2b)=0 are, when ab+bc+ca=0

If the equation a x^2+b x+c=0 has two positive and real roots, then prove that the equation a x^2+(b+6a)x+(c+3b)=0 has at least one positive real root.

If a+b+c=0 and a,b,c are rational. Prove that the roots of the equation (b+c-a)x^(2)+(c+a-b)x+(a+b-c)=0 are rational.

Prove that the roots of the equation (a^4+b^4)x^2+4a b c dx+(c^4+d^4)=0 cannot be different, if real.

Prove that the roots of the equation (a^4+b^4)x^2+4a b c dx+(c^4+d^4)=0 cannot be different, if real.

If the roots of the equation (b-c)x^2+(c-a)x+(a-b)=0 are equal then a,b,c will be in

CENGAGE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. Consider the graph of y = f(x) as shown in the following figure. ...

    Text Solution

    |

  2. If x^2+p x-444p=0 has integral roots where p is prime number, then fin...

    Text Solution

    |

  3. The equation a x^2+b x+c=0 has real and positive roots. Prove that th...

    Text Solution

    |

  4. If the roots of the equation x^2-ax+b=0y are real and differ b a quan...

    Text Solution

    |

  5. If (a x^2+b x+c)y+(a^(prime)x^2+b^(prime)x^2+c^(prime))=0 and x is a r...

    Text Solution

    |

  6. Show that the minimum value of (x+a)(x+b)//(x+c) where a > c ,b > c , ...

    Text Solution

    |

  7. Let a ,b in N and a > 1. Also p is a prime number. If a x^2+b x+c=p f...

    Text Solution

    |

  8. If 2x^2-3x y-2y^2=7, then prove that there will be only two integral p...

    Text Solution

    |

  9. If a and c are odd prime numbers and a x^2+b x+c=0 has rational roots ...

    Text Solution

    |

  10. If f(x)=x^3+b x^2+c x+d and f(0),f(-1) are odd integers, prove that f...

    Text Solution

    |

  11. If x is real, then the maximum value of y=2(a-x)(x+sqrt(x^2+b^2))

    Text Solution

    |

  12. If equation x^4-(3m+2)x^2+m^2=0(m >0) has four real solutions which ar...

    Text Solution

    |

  13. Number of positive integers x for which f(x)=x^3-8x^2+20 x-13 is a pri...

    Text Solution

    |

  14. If set of values a for which f(x)=a x^2-(3+2a)x+6, a!=0 is positive fo...

    Text Solution

    |

  15. Polynomial P(x) contains only terms of aodd degree. when P(x) is divid...

    Text Solution

    |

  16. If the equation 2x^2+4x y+7y^2-12 x-2y+t=0, where t is a parameter has...

    Text Solution

    |

  17. Let alpha1,beta1 be the roots x^2-6x+p=0a n d alpha2,beta2 be the root...

    Text Solution

    |

  18. If sqrt(sqrt(sqrt(x)))=(3x^4+4)^(1/64), then the value of x^4 is.

    Text Solution

    |

  19. Let P(x)=x^4+a x^3+b x^2+c x+d be a polynomial such that P(1)=1,P(2)=8...

    Text Solution

    |

  20. If the equation x ^2+2(lambda+1)x+lambda^2+lambda+7=0 has only negati...

    Text Solution

    |