Home
Class 12
MATHS
If x+1 is a factor of x^(3)-5x^(2)+kx+2,...

If `x+1` is a factor of `x^(3)-5x^(2)+kx+2`, then k=

A

`-4`

B

`-2`

C

`0`

D

2

Text Solution

Verified by Experts

The correct Answer is:
A
If x+1 is a factor of `x^(3)-5x^(2)+kx+2`, then dividing `x^(3)-5x^(2)+kx+2` by x+1 leaves a remainder of 0. use synthetic division:

Since -k-4=0,k=-4,[4].
Promotional Banner

Topper's Solved these Questions

  • COUNTING

    ENGLISH SAT|Exercise EXERCISE|10 Videos

  • ELEMENTARY ALGEBRA

    ENGLISH SAT|Exercise EXERCISE|12 Videos

Similar Questions

Explore conceptually related problems

If x-4 is a factor of x^(2)-kx+2k , where k is a constant, what is the value of k?

If x+1 is a factor of the polynomial 2x^(2)+kx, then the value of k is

(i) If 2x + 1 is a factor of 2x^2+ ax- 3, find the value of a. (ii) Find the value of k, if 3x -4 is a factor of expression 3x^2+ 2x -k.

Using the Factor theorem, show that (i) (x-2) is a factor of x^(3)-2x^(2)-9x+18 . Hence factorise the expression x^2-2x^2-9x+18 completely. (ii) (x+5) is a factor of 2x^3+5x^2-28x-15 . Hence factorise the expression 2x^3+5x^2-28x-15 completely. (iii) (3x+2) is a factor of 3x^(3)+2x^(2)-3x-2 . Hence factorise the expression 3x^3+2x^2-3x-2 completely.

If x+1 is a factor of the polynomial 2x^2+k x , then k= (a) -2 (b) -3 (c) 4 (d) 2

Show that : (i) x-5, is factor of x^(2)-11x+30 " " (ii) (x+2 , is a factor of x^(2)+3x+2 (iii) x-3, is a factor of 2x^(3)+7x^(2)-24x-45 " " (iv) 3x-2 , is a factor of 3x^(3)+x^(2)-20x+12 (v) x-1, is a factor of x^(3)-10x^(2)+23x-14 " " (vi) x-2 , is a factor of x^(3)-3x^(2)-x+6

Find the value of 'k' if (x-2) is a factor of x^3+2x^2-kx+10 . Hence determine whether (x+5) is also a factor.

Find the value of 'k' if : (i) x+5, is a factor of 2x^(3)+kx^(2)-11x-30 " " (ii) 2x-1 , is a factor of 2x^(3)-7x^(2)+11x-7+k

ENGLISH SAT-DIAGNOSTIC TEST -MCQs (EXERCISE)
  1. How many integers are there in the solution set of |x-2|le5?

    Text Solution

    |

  2. If f(x)=sqrt(x^(2)), then f(x) can also be expressed as

    Text Solution

    |

  3. If x+1 is a factor of x^(3)-5x^(2)+kx+2, then k=

    Text Solution

    |

  4. George invests $1,000 into an account that he hopes will earh 12% inte...

    Text Solution

    |

  5. A linear function has an x-intercept of sqrt(3) and a y-intercept of s...

    Text Solution

    |

  6. If f(x)=2x-1, find the value of x that makes f(f(x))=9.

    Text Solution

    |

  7. The plane 2x+3y-4z=5 intersects the x-axis at (a,0,0), the y-axis at (...

    Text Solution

    |

  8. Given the set of data 1,1,2,2,2,3,3,4, which one of the following stat...

    Text Solution

    |

  9. If (x-3y)/(x)=7, what is the value of (x)/(y)?

    Text Solution

    |

  10. Find all values of x that make |(2,-1,4),(3,0,5),(4,1,6)|=|(x,4),(5,x)...

    Text Solution

    |

  11. Suppose f(x)=(1)/(2)x^(2)-8 for -4lexle4. Then the maximum value of th...

    Text Solution

    |

  12. If tantheta=(2)/(3), then sintheta=

    Text Solution

    |

  13. Suppose the graph of f(x)=-x^(3) is translated 4 units right and 2 uni...

    Text Solution

    |

  14. i^(2014)=

    Text Solution

    |

  15. The statistics below provide a summary of IQ scores of 100 children. ...

    Text Solution

    |

  16. If f(x)=secx, then

    Text Solution

    |

  17. The polar coordinates of a point P are (2,200^(@)) The rectangular coo...

    Text Solution

    |

  18. The height of a cone is equal to the radius of its base. The radius of...

    Text Solution

    |

  19. In how many distinguishable ways can the seven letters in the word MIN...

    Text Solution

    |

  20. Which of the following lins are asymptotes of the graph of y=(x)/(x+1)...

    Text Solution

    |