Home
Class 11
MATHS
Find the non-zero roots of the equation....

Find the non-zero roots of the equation.
`(i) Delta=|{:(,a,b,ax+b),(,b,c,bx+c),(,ax+b,bx+c,c):}|=0`

A

a,b ,c are in A.P

B

a, b, c are in G.P

C

a, b, c are in H.P

D

`alpha` is a root of `ax^(2) + bx + c = 0`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|30 Videos

  • DETERMINANTS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section II - Assertion Reason Type|6 Videos

  • CARTESIAN CO-ORDINATE SYSTEM

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|27 Videos

  • DISCRETE PROBABILITY DISTRIBUTIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|40 Videos

Similar Questions

Explore conceptually related problems

If a >0 and discriminant of a x^2+2b x+c is negative, then Delta = |(a,b,ax +b),(b,c,bx +c),(ax +b,bx +c,0)| is a. +v e b. (a c-b)^2(a x^2+2b x+c) c. -v e d. 0

If a^(2) + b^(2) = c^(2), c != 0 , then find the non-zero solution of the equation: sin^(-1).(ax)/(c) + sin^(-1).(bx)/(c) = sin^(-1) x

If both the roots of the equation ax^(2) + bx + c = 0 are zero, then

If sin theta and -cos theta are the roots of the equation ax^(2) - bx - c = 0 , where a, b, and c are the sides of a triangle ABC, then cos B is equal to

Let alpha , beta (a lt b) be the roots of the equation ax^(2)+bx+c=0 . If lim_(xtom) (|ax^(2)+bx+c|)/(ax^(2)+bx+c)=1 then

If alpha,beta are the roots of the equation ax^2 + bx+c=0 then the roots of the equation (a + b + c)x^2-(b + 2c)x+c=0 are (a) c (b) d-c (c) 2c (d) 0

If alpha and beta are the roots of the equation ax ^(2) + bx + c=0,a,b, c in R , alpha ne 0 then which is (are) correct:

Assertion (A): The roots of the equation a(b-c)x^(2)+b(c-a)x+c(a-b)=0 are 1, (c(a-b))/(a(b-c)) Reason (R): If a+b+c=0 then the roots of ax^(2)+bx+c=0 are 1, (c)/(a)

If alpha and beta , alpha and gamma , alpha and delta are the roots of the equations ax^(2)+2bx+c=0 , 2bx^(2)+cx+a=0 and cx^(2)+ax+2b=0 respectively where a , b , c are positive real numbers, then alpha+alpha^(2) is equal to

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

OBJECTIVE RD SHARMA ENGLISH-DETERMINANTS-Exercise
  1. The determinant Delta =|{:(a^(2)+x,,ab,,ac),(ab,,b^(2)+x,,bc),(ac,,bc...

    Text Solution

    |

  2. If r=|2^r 2.3^r-1 4.5^r-1alphabetagamma2^n-1 3^n-1 5^n-1| , then find ...

    Text Solution

    |

  3. Find the non-zero roots of the equation. (i) Delta=|{:(,a,b,ax+b),(,...

    Text Solution

    |

  4. Let Delta(a)=|{:((a-1),n,6),((a-1)^(2), 2n^(2),4m-2),((a-1)^(3),3n^(3)...

    Text Solution

    |

  5. if a(1),a(2),…….a(n),……. form a G.P. and a(1) gt 0 , for all I ge 1 ...

    Text Solution

    |

  6. For x ne y ne z , |{:(1+x^(3),,x^(2),,1),(1+y^(3),,y^(2),,1),(1+z^(3...

    Text Solution

    |

  7. " if " |{:(b+c,,c+a,,a+b),(a+b,,b+c,,c+a),(c+a,,a+b,,b+c):}|=k |{:(a...

    Text Solution

    |

  8. If A is a square matrix of order n such that its elements are polynomi...

    Text Solution

    |

  9. Prove the identities: |{:(b^(2)+c^(2),,ab,,ac),(ab,,c^(2)+a^(2),,bc),...

    Text Solution

    |

  10. a^(−1)+b^(−1)+c^(−1)=0 such that |[1+a,1,1,],[1,1+b,1,],[1,1,1+c,]| =△...

    Text Solution

    |

  11. If alpha,beta,gamma are real numbers, then without expanding at any...

    Text Solution

    |

  12. If A,B,C are the angles of triangle ABC, then the minimum value of |{:...

    Text Solution

    |

  13. If x, y , z are in A.P., then the value of the det (A) is , where A ...

    Text Solution

    |

  14. Find the number of real root of the equation |0x-a x-b x+a0x-c x+b x+c...

    Text Solution

    |

  15. If a , b , c are distinct, then the value of x satisfying |0x^2-a x^3-...

    Text Solution

    |

  16. Let the following system of equations {:(kx+y+z=1),(x+ky+z=k),(x+y+k...

    Text Solution

    |

  17. Show that: |b^2+c^2a b a c b a c^2+a^2b c c a c b a^2+b^2|=4a^2b^2c^2

    Text Solution

    |

  18. Let triangle =|[2a1b1, a1b2+a2b1, a1b3+a3b1], [a1b2+a2b1, 2a2b2, a2b3+...

    Text Solution

    |

  19. If B is a non-sinfular matrix and A is square matrix, then det B^(-1)A...

    Text Solution

    |

  20. If 0 lt theta lt pi and the system of equations (sin theta) x + y + ...

    Text Solution

    |