Home
Class 12
MATHS
Consider the determinant f(x)=|0x^2-a x^...

Consider the determinant `f(x)=|0x^2-a x^3-b x^2+a0x^2+c x^4+b x-c0|dot` Statement 1: `f(x)=0` has one root `x=0.` Statement 2: The value of skew symmetric determinant of odd order is always zero.

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • DETERMINANT

    CENGAGE ENGLISH|Exercise Multiple Correct Answer|5 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE ENGLISH|Exercise Multiple correct answers type|11 Videos

Similar Questions

Explore conceptually related problems

Consider the determinant f(x)=|{:(0,x^(2)-a,x^(3)-b),(x^(2)+a,0,x^(2)+c),(x^(4)+b,x-c,0):}| Statement -1 f(x) =0 has one root x =0. Statement -2 The value of skew -symmetric determinant of odd order is always zero.

If f(x)=|(0, x-a, x-b), (x+a, 0, x-c),(x+b, x+c, 0)| , then

If f(x)=|0x-a x-b x+a0x-c x+b x+c0|,t h e n f(x)=0 (b) f(b)=0 (c) f(0)=0 f(1)=0

Statement -1: f(x) = x^(3)-3x+1 =0 has one root in the interval [-2,2]. Statement-2: f(-2) and f(2) are of opposite sign.

If f(x)=|{:(0,x-a,x-b),(x+a,0,x-c),(x+b,x+c,0):}| , then

If a , b , c are distinct, then the value of x satisfying |0x^2-a x^3-b x^2+a0x^2+c x^4+b x-c0|=0i s c (b) a (c) b (d) 0

Consider the matrix A=[{:(0,-h,-g),(h,0,-f),(g,f, 0):}] STATEMENT-1 : Det A = 0 STATEMENT-2 :The value of the determinant of a skew symmetric matrix of odd order is always zero.

If a ,b ,c are different, then the value of |[0,x^2-a, x^3-b],[ x^2+a,0,x^2+c],[ x^4+b, x-c,0]| is a. c b. a c. b d. 0

Find the number of real root of the equation |0x-a x-b x+a0x-c x+b x+c0|=0,a!=b!=ca n db(a+c)> a c

Let f(x)=x+2|x+1|+2|x-1|dot If f(x)=k has exactly one real solution, then the value of k is (a) 3 (b) 0 (c) 1 (d) 2

CENGAGE ENGLISH-DETERMINANTS-All Questions
  1. For a concave mirror, if real image is formed the graph between (1)/(u...

    Text Solution

    |

  2. Prove that the determinant |[x, sintheta,costheta],[-sintheta,-x,1],[...

    Text Solution

    |

  3. Consider the determinant f(x)=|0x^2-a x^3-b x^2+a0x^2+c x^4+b x-c0|dot...

    Text Solution

    |

  4. Find the value of |[1, 2, 4],[-1,3, 0],[4 ,1, 0]|

    Text Solution

    |

  5. Consider the system of the equation k x+y+z=1,x+k y+z=k ,a n dx+y+k z=...

    Text Solution

    |

  6. If x+y+z=0 prove that |[a x, b y, c z],[ c y, a z ,b x],[ b z ,c x ,a ...

    Text Solution

    |

  7. Each question has four choices a, b, c and d, out of which only one is...

    Text Solution

    |

  8. If a ,b ,c in R , then find the number of real roots of the equat...

    Text Solution

    |

  9. Delta = |(a, a^2, 0),(1, 2a+b,(a+b)),(0, 1, 2a+3b)| is divisible by a....

    Text Solution

    |

  10. Without expanding at any stage, prove that the value of each of the...

    Text Solution

    |

  11. If a,b,c are positive and are the pth, qth rth terms respectively of a...

    Text Solution

    |

  12. If the entries in a 3xx3 determinant are either 0 or 1, then the grea...

    Text Solution

    |

  13. The value of the determinant of n^(t h) order, being given by |[x, 1, ...

    Text Solution

    |

  14. Prove that a!=0,|[x+a, x,x],[x,x+a,x],[x,x,x+a^2]|=0 represents a stra...

    Text Solution

    |

  15. If =|[a b c, b^2c,c^2b],[ a b c,c^2a, c a^2],[a b c, a^2b,b^2a]|=0,(a ...

    Text Solution

    |

  16. The value of |[yz, z x,x y],[ p,2p,3r],[1, 1, 1]|,w h e r ex ,y ,z ar...

    Text Solution

    |

  17. Show that the determinant |a^2+b^2+c^2b c+c a+a bb c+c a+a bb c+c a+a ...

    Text Solution

    |

  18. If x!=0,y!=0,z!=0 and |[1+x,1,1],[1+y,1+2y,1],[1+z,1+z,1+3z]|=0, then ...

    Text Solution

    |

  19. If x!=y!=za n d|[x,x^2, 1+x^3],[y ,y^2 ,1+y^3],[z, z^2, 1+z^3]|=0, th...

    Text Solution

    |

  20. Prove that |2alpha+beta+gamma+deltaalphabeta+gammadelta alpha+beta+g...

    Text Solution

    |