Home
Class 12
MATHS
If equation (lamda^(2)-5lamda+6)x^(2)+(l...

If equation `(lamda^(2)-5lamda+6)x^(2)+(lamda^(2)-3lamda+2)x+(lamda^(2)-4)=0` is satisfied by more than two values of `x`, find the parameter `lamda`.

Text Solution

Verified by Experts

If an equation of degree to is satisfied by more than two values of unknown, then it must be an identity. Then, we must have
`lamda^(2)-5lamda+6=0,lamda^(2)-3lamda+2=0lamda^(2)-4=0`
`implieslamda=2,3` and `lamda=2,1` and `lamda=2,-2`
Common value of `lamda` which satisfies each condition is `lamda=2`.
Promotional Banner

Topper's Solved these Questions

  • THEORY OF EQUATIONS

    ARIHANT MATHS|Exercise Exercise For Session 1|11 Videos

  • THEORY OF EQUATIONS

    ARIHANT MATHS|Exercise Exercise For Session 2|10 Videos

  • THE STRAIGHT LINES

    ARIHANT MATHS|Exercise The Straight Lines Exercise 8 : (Questions Asked in Previous 13 years Exams)|1 Videos

  • THREE DIMENSIONAL COORDINATE SYSTEM

    ARIHANT MATHS|Exercise Three Dimensional Coordinate System Exercise 12 : Question Asked in Previous Years Exam|2 Videos

Similar Questions

Explore conceptually related problems

If alpha, beta are the roots fo the equation lamda(x^(2)-x)+x+5=0 . If lamda_(1) and lamda_(2) are two values of lamda for which the roots alpha, beta are related by (alpha)/(beta)+(beta)/(alpha)=4/5 find the value of (lamda_(1))/(lamda_(2))+(lamda_(2))/(lamda_(1))

IF lamda^(log_(5)3 =81 ,find the value of lamda .

If the following equations x+y-3z = 0, (1+lamda)x + (2+lamda) y - 8z = 0, x-(1+lamda)y + (2+lamda)z = 0 are consistent then the value of lamda is

Evaluate |(x+lamda,x,x),(x,x+lamda,x),(x,x,x+lamda)|

If both the roots of lamda(6x^(2)+3)+rx+2x^(2)-1=0 and 6 lamda(2x^(2)+1)+px+4x^(2)-2=0 are common, then 2r-p is equal to

It is known that x=9 is root of the equation. log_lamda(x^2+15a^2)-log_lamda(a-2)=log_lamda "(8ax)/(a-2) find the other roots of this equation.

Let f(x,y)=0 be the equation of a circle. If f(0,lamda)=0 has equal roots lamda=2,2 and f(lamda,0)=0 has roots lamda=(4)/(5),5 then the centre of the circle is

If cos^(-1) lamda + cos^(-1) mu + cos^(-1) gamma = 3pi , then find the value of lamda mu + mu gamma + gamma lamda

Find the value of lamda so that the equations x^(2)-x-12=0 and lamdax^(2)+10x+3=0 may have one root in common. Also, find the common root.

If product of the real roots of the equation, x^(2)-ax+30=2sqrt((x^(2)-ax+45)),agt0 is lamda minimum value of sum of roots of the equation is mu . The value of (mu) (where (.) denotes the least integer function) is

ARIHANT MATHS-THEORY OF EQUATIONS-Exercise (Questions Asked In Previous 13 Years Exam)
  1. If equation (lamda^(2)-5lamda+6)x^(2)+(lamda^(2)-3lamda+2)x+(lamda^(2)...

    Text Solution

    |

  2. In the quadratic equation ax^2 + bx + c = 0. if delta = b^2-4ac and al...

    Text Solution

    |

  3. Let S denote the set of all polynomials P(x) of degree lt=2 such th...

    Text Solution

    |

  4. If the roots of x^2-b x+c=0 are two consecutive integers, then b^2-4c ...

    Text Solution

    |

  5. If the equation a(n)x^(n)+a(n-1)x^(n-1)+..+a(1)x=0, a(1)!=0, n ge2, ha...

    Text Solution

    |

  6. If both the roots of the quadratic equation x^(2)-2kx+k^(2)+k-5=0 are ...

    Text Solution

    |

  7. Let a and b be the roots of the equation x^2-10 c x-11 d=0 and those ...

    Text Solution

    |

  8. Let a,b,c be the sides of a triangle. No two of them are equal and lam...

    Text Solution

    |

  9. All the value of m for which both the roots of the equation x 2 −2mx...

    Text Solution

    |

  10. If the roots of the quadratic equation x^2+p x+q=0 are tan30^0a n dtan...

    Text Solution

    |

  11. Let alpha,beta be the roots of the equation x^2-p x+r=0a n dalpha//2,2...

    Text Solution

    |

  12. If the difference between the roots of the equation x^2+a x+1=0 is les...

    Text Solution

    |

  13. Let a ,b , c ,p ,q be real numbers. Suppose alpha,beta are the roots o...

    Text Solution

    |

  14. The quadratic equations x^2""-6x""+""a""=""0""a n d ""x^2""-c x""+""...

    Text Solution

    |

  15. How many real solutions does the equation x^7+14 x^5+16 x^3+30 x-560=0...

    Text Solution

    |

  16. Suppose the cubic x^(3)-px+q has three distinct real roots, where pgt0...

    Text Solution

    |

  17. Find the discriminant of the quadratic equation 2x^2-4x+3=0, and hence...

    Text Solution

    |

  18. If the roots of the equation b x^2+""c x""+""a""=""0 be imaginary, t...

    Text Solution

    |

  19. Let p and q real number such that p!= 0,p^3!=q and p^3!=-q. if alpha a...

    Text Solution

    |

  20. solve 0=-1+2x+3x^2

    Text Solution

    |

  21. Find the roots of x^2-6x-2=0

    Text Solution

    |