Home
Class 11
MATHS
If the roots of the equation x^2-ax+b=0y...

If the roots of the equation `x^2-ax+b=0`y are real and differ b a quantity which is less than `c(c >0),` then show that `b` lies between `(a^2-c^2)/4` and `a^2/4.`

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

If a,b, cinR , show that roots of the equation (a-b)x^(2)+(b+c-a)x-c=0 are real and unequal,

6.The roots of the equation (a-b+c)x^(2)+4(a-b)x+(a-b-c)=0 are

If the roots of the equation ax^(2)+bx+c=0 be in the ratio 3:4, show that 12b^(2)=49ac .

If the roots of the equation ax^2 + bx + c = 0, a != 0 (a, b, c are real numbers), are imaginary and a + c < b, then

If the roots of the equation a(b-c)x^2+b(c-a)x+c(a-b)=0 are equal, show that 2//b=1//a+1// c dot

If the roots of the equation a(b-c)x^2+b(c-a)x+c(a-b)=0 are equal, show that 2//b=1//a+1//cdot

If the roots of the equation x^2+2c x+a b=0 are real unequal, prove that the equation x^2-2(a+b)x+a^2+b^2+2c^2=0 has no real roots.

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.

The number of real roots of the equation x^2tanx=1 lies between 0 and 2pi is/are (A) 1 (B) 2 (C) 3 (D) 4

CENGAGE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. If x^2+p x-444p=0 has integral roots where p is prime number, then fin...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  4. 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

    |

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

    Text Solution

    |

  6. 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

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  18. 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

    |

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

    Text Solution

    |

  20. Given alphaa n dbeta are the roots of the quadratic equation x^2-4x+k...

    Text Solution

    |