Home
Class 11
MATHS
If the equations x^2+p x+q=0 and x^2+p^(...

If the equations `x^2+p x+q=0 and x^2+p^(prime)x+q^(prime)=0` have a common root, then it must be equal to

a.`(p^(prime)-p ^(prime) q)/(q-q^(prime))`

b. `(q-q ')/(p^(prime)-p)`

c. `(p^(prime)-p)/(q-q^(prime))`

d. `(p q^(prime)-p^(prime) q)/(p-p^(prime))`

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 the equation x^2+px+q=0 and x^2+p'x+q'=0 have a common root , prove that , it is either (pq'-p'q)/(q'-q) or, (q'-q)/(p'-p) .

If x^2+p x+q=0a n dx^2+q x+p=0,(p!=q) have a common roots, show that 1+p+q=0 .

If (a x^2+b x+c)y+(a^(prime)x^2+b^(prime)x+c^(prime))=0 and x is a rational function of y , then prove that (a c^(prime)-a^(prime)c)^2=(a b^(prime)-a^(prime)b)xx(b c^(prime)-b^(prime)c)dot

If the roots of the equation x^2+2px+q=0 and x^2+2qx+p=0 where p!=q .Differ by a constant ,prove that p+q+1=0

IF 2+sqrt3i is a root of the equation x^2+px+q=0 where p and q are real, find p and q.

If the roots of the quadratics x^2 - qx +p = 0 and x^2 - px + q = 0 (p!= q) differ by a constant, show.that p + q + 4 = 0.

Simply (a^(p)/a^(q))^(p+q-r).(a^(q)/a^(r ))^(q+r-p).(a^(r )/a^(p))^(r+p-q)

If the roots of the equation p(q-r)x^2+q(r-p)x+r(p-q)=0 be equal ,show that 1/p+1/r=2/q

If the equation x^2-3p x+2q=0a n dx^2-3a x+2b=0 have a common roots and the other roots of the second equation is the reciprocal of the other roots of the first, then (2q-2b)^2 . a. 36p a(q-b)^2 b. 18p a(q-b)^2 c. 36b q(p-a)^2 d. 18b q(p-a)^2

If , p , q are the roots of the equation x^(2)+px+q=0 , then

CENGAGE PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. If z0 is the circumcenter of an equilateral triangle with vertices z1,...

    Text Solution

    |

  2. Two different non-parallel lines cut the circle |z| = r at points a...

    Text Solution

    |

  3. If the equations x^2+p x+q=0 and x^2+p^(prime)x+q^(prime)=0 have a com...

    Text Solution

    |

  4. Prove that |z-z1|^2+|z-z2|^2=k will represent a real circle with cente...

    Text Solution

    |

  5. Complex numbers z1 , z2 , z3 are the vertices A, B, C respectively of ...

    Text Solution

    |

  6. Given that alpha,gamma are roots of the equation A x^2-4x+1=0,a n dbet...

    Text Solution

    |

  7. The area of the triangle in the complex plane formed by the points z, ...

    Text Solution

    |

  8. Intercept made by the circle zbar z +bar az+abar z+r=0 on the real a...

    Text Solution

    |

  9. The graph of the quadratic trinomial y=a x^2+b x+c has its vertex at (...

    Text Solution

    |

  10. if iz^3+z^2-z+i=0 then show that absz=1

    Text Solution

    |

  11. Show that the equation of a circle passing through the origin and ha...

    Text Solution

    |

  12. The function f(x)=a x^3+b x^2+c x+d has three positive roots. If the ...

    Text Solution

    |

  13. let z1=10+6i and z2=4+6i if z is nay complex number such that argument...

    Text Solution

    |

  14. Let vertices of an acute-angled triangle are A(z1),B(z2),a n dC(z3)dot...

    Text Solution

    |

  15. If (18x^2+12x+4)^n = a0 +a(1x)+ a(2x)^2 +......+ a(2n)x^(2n), prove th...

    Text Solution

    |

  16. If z=z0+A( bar z -( bar z 0)), w h e r eA is a constant, then prove t...

    Text Solution

    |

  17. If (sinalpha)x^2-2x+bgeq2 for all real values of xlt=1a n dalpha in (0...

    Text Solution

    |

  18. If z1, z2, z3 are three complex numbers such that 5z1-13 z2+8z3=0, t...

    Text Solution

    |

  19. If one root x^2-x-k=0 is square of the other, then k= a.2+-sqrt(5)...

    Text Solution

    |

  20. If z1, z2 are complex number such that (2z1)/(3z2) is purely imaginary...

    Text Solution

    |