Home
Class 10
MATHS
If the polynomial 6x^4+8x^3+17 x^2+21 x+...

If the polynomial `6x^4+8x^3+17 x^2+21 x+7` is divided by another polynomial `3x^2+4x+1,` the remainder comes out to be `a x+b`, find `a and b`.

Text Solution

Verified by Experts

When we divide `6x^4+8x^3+17 x^2+21 x+7` by another polynomial `3x^2+4x+1`
we get `2x^2+5` as quotient
so,we know,
Dividend = Divisor `xx` Quotient + Remainder
Substituting the values in this equation,
...
Promotional Banner

Topper's Solved these Questions

  • PAIR OF LINEAR EQUATIONS IN TWO VARIABLES

    RD SHARMA|Exercise All Questions|390 Videos

  • PROBABILITY

    RD SHARMA|Exercise All Questions|183 Videos

Similar Questions

Explore conceptually related problems

If the polynomial 6x^4 +8 x^3 +17 x^2 +21x +7 is divided by another polynomial 3 x^2 + 4x +1;the remainder comes out to be ax+b. Find a and b.

If the polynomial 6x^4 +8 x^3 +17 x^2 +21x +7 is divided by another polynomial 3 x^2 + 4x +1;the remainder comes out to be ax+b .Find a and b.

If the polynomial 6x^(4)+8x^(3)+17x^(2)+25x-9 is divided by another polynomial 3x^(2)+4x+1 , the remainder comes out to be a+bx, find (a+b)^(2) .

If the polynomial f(x)=x^(4)-6x^(3)+16x^(2)-25x+10 is divided by another polynomial x^(2)-2x+k the remainder comes out to be x+a, find k and a.

If the polynomial x^(4)-6x^(3)+16x^(2)-25x+10 is divided by another polynomial x^(2)-2x+k , the remainder comes out to be (x-a). Find k and a.

If the polynomial x^(4)-6x^(3)+16x^(2)-25x+10 is divided by another polynomial x^(2)-2x+k, the remainder copies out to be x+a* find k and a.

If the polynomial (x^(4)+2x^(3)+8x^(2)+12x+18) is divided by another polynomial (x^(2)+5) , the remainder comes out to be (px+q) . Find the values of p and q .

If the polynomial (x^(4)+2x+8x^(2)+12x+18) is divided by another polynomial (x^(2)+5) , the remainder comes out to be (px+q). Find the values of p and q.

Divide the polynomial 3x^(4)-4x^(3)-3x-1 by x-2

Divide the polynomial 6x^(4) - 44x^(2) + 6x - 3 by the polynomial x^(2) - 3x + 1 and verify the division algorithm.

RD SHARMA-POLYNOMIAL-All Questions
  1. Find the values of a and b so that x^4+x^3+8x^2+a x+b is divisible by ...

    Text Solution

    |

  2. Find all zeros of the polynomial 2x^4+7x^3-19 x^2-14 x+30 , if two of ...

    Text Solution

    |

  3. If the polynomial 6x^4+8x^3+17 x^2+21 x+7 is divided by another polyno...

    Text Solution

    |

  4. If alpha,beta,gamma are the zeros of the polynomial f(x)=x^3-p x^2+q x...

    Text Solution

    |

  5. If alpha,beta are the zeros of the polynomial f(x)=a x^2+b x+c , then ...

    Text Solution

    |

  6. If alpha,beta are the zeros of the polynomial f(x)=a x^2+b x+c , then ...

    Text Solution

    |

  7. Divide the polynomial f(x)=3x^2-x^3-3x+5 by the polynomial g(x)=x-1and...

    Text Solution

    |

  8. Draw the graph of the polynomial f(x)=2x-<5 Also, find the coordinates...

    Text Solution

    |

  9. Draw the graph of the polynomial f(x)=x^2-2

    Text Solution

    |

  10. Draw the graph of the quadratic polynomial f(x)=3-2x-x=2

    Text Solution

    |

  11. If alpha and beta are the zeros of the polynomial f(x)=x^2+p x+q, form...

    Text Solution

    |

  12. Draw the graph of the polynomial f(x)=-42+4x-1. Also find the vertex o...

    Text Solution

    |

  13. If the sum of the zeros of the quadratic polynomial f(t)=k t^2+2t+3k i...

    Text Solution

    |

  14. Draw the graph of the polynomial f(x)=-3x^2+x.

    Text Solution

    |

  15. Find the zeros of the quadratic polynomial x^2+7x+12 , and verify the ...

    Text Solution

    |

  16. Find the zeros of polynomial f(x) = 4sqrt3 x^2 + 5x - 2sqrt 3; and ver...

    Text Solution

    |

  17. If alpha and beta are the zeros of the quadratic polynomial f(x)=x^2-p...

    Text Solution

    |

  18. Obtain all the zeros of the polynomial f(x)=3x^4+6x^3−2x^2−10x−5, if ...

    Text Solution

    |

  19. What must be subtracted from 8x^4+14 x^3-2x^2+7x-8 so that the resulti...

    Text Solution

    |

  20. By applying division algorithm prove that the polynomial g(x)=x^2+3x+1...

    Text Solution

    |