Home
Class 11
MATHS
If sintheta,costheta be the roots of a x...

If `sintheta,costheta` be the roots of `a x^2+b x+c=0` , then prove that `b^2=a^2+2ac dot`

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 tantheta and sectheta are the roots of a x^2+b x+c=0, then prove that a^4=b^2(b^2-4ac)dot

If sintheta and costheta are the roots of the equation ax^2-bx+c=0 , then a, b and c satisfy the relation

If sin theta,costheta are the roots of the equation ax^2+bx+c =0 then find the value of (a+c)^2/(b^2+c^2)

If the ratio of the roots of the equation x^2+p x+q=0 are equal to ratio of the roots of the equation x^2+b x+c=0 , then prove that p^2c=b^2qdot

Let alpha and beta be the roots of the equation ax^2+2bx+c =0 and alpha+gamma and beta+gamma be the roots of Ax^2+2Bx+C =0. Then prove that A^2(b^2-ac)=a^2(B^2-AC) .

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 alpha,beta are the nonzero roots of a x^2+b x+c=0 and alpha^2,beta^2 are the roots of a^2x^2+b^2x+c^2=0 , then a ,b ,c are in (A) G.P. (B) H.P. (C) A.P. (D) none of these

If alpha,beta are the roots of a x^2+b x+c=0,(a!=0) and alpha+delta,beta+delta are the roots of A x^2+B x+C=0,(A!=0) for some constant delta then prove that (b^2-4a c)/(a^2)=(B^2-4A C)/(A^2)

If alpha and beta are roots of ax^2+bx+c =0 then prove that (alpha/beta+beta/alpha) = ((b^2-2ac)/(ac))

If the ratio of the roots of the quadratic equation ax^(2)+bx+c=0 be m:n, then prove that ((m+n)^2)/(mn)=(b^(2))/(ac)

CENGAGE PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. If the ratio of the roots of the equation x^2+p x+q=0 are equal to rat...

    Text Solution

    |

  2. Let z=1-t+isqrt(t^2+t+2), where t is real parameter. The locus of z in...

    Text Solution

    |

  3. If sintheta,costheta be the roots of a x^2+b x+c=0 , then prove that b...

    Text Solution

    |

  4. Express the following complex numbers in a+i b form: ((3-2i)(2+3i))/((...

    Text Solution

    |

  5. If a ,b ,c are nonzero real numbers and a z^2+b z+c+i=0 has purely i...

    Text Solution

    |

  6. z^2+zabsz+absz^2=0 then the locus of z is

    Text Solution

    |

  7. If the sum of the roots of the equation 1/(x+a)+1/(x+b)=1//c is zero,...

    Text Solution

    |

  8. Solve the equation x^2+p x+45=0. it is given that the squared differen...

    Text Solution

    |

  9. Find the least positive integer n such that ((2i)/(1+i))^n is a positi...

    Text Solution

    |

  10. z1a n dz2 lie on a circle with center at the origin. The point of inte...

    Text Solution

    |

  11. If alpha,beta are the roots of the equation 2x^2-35x+2=0 , the find ...

    Text Solution

    |

  12. If one root of the equation z^2-a z+a-1= 0 is (1+i), where a i...

    Text Solution

    |

  13. If |z1|=|z2|=|z3|=1 and z1+z2+z3=0 then the area of the triangle whose...

    Text Solution

    |

  14. Simplify: (sqrt(5+12 i)+sqrt(5-12 i))/(sqrt(5+12 i)-sqrt(5-12 i))

    Text Solution

    |

  15. Find a quadratic equation whose product of roots x1 and x2 is equa...

    Text Solution

    |

  16. If sqrt(5-12 i)+sqrt(-5-12 i)=z , then principal value of a rgz can be

    Text Solution

    |

  17. If (x+i y)(p+i q)=(x^2+y^2)i , prove that x=q ,y=pdot

    Text Solution

    |

  18. If a and b(!=0) are the roots of the equation x^2+a x+b=0, then find...

    Text Solution

    |

  19. Let A ,B ,C ,D be four concyclic points in order in which A D : A B=C ...

    Text Solution

    |

  20. Convert (1+3i)/(1-2i) into the polar form.

    Text Solution

    |