Home
Class 12
MATHS
Let p(x) = x^2+bx+c, where b and c are i...

Let `p(x) = x^2+bx+c`, where b and c are integers. If p(x) is a factor of both `x^4+6x^2 +25 and 3x^4+4x^2+28x+5`, find the value of p(1).

Text Solution

Verified by Experts

The correct Answer is:
4
Promotional Banner

Topper's Solved these Questions

  • JEE MOCK TEST 4

    NTA MOCK TESTS|Exercise MATHEMETIC - SUBJECTIVE NUMERICAL|5 Videos

  • JEE MOCK TEST 6

    NTA MOCK TESTS|Exercise MATHEMATICS|25 Videos

Similar Questions

Explore conceptually related problems

let P(x)=x^(2)+bx+c, wherer b and c are interger.if P(x) is a factor of both x^(4)+6x^(2)+25 and 3x^(2)+4x^(2)+28x+5 find value of p(1)

Let f(x)=x^(2)+bx+c, where b,c in R. If f(x) is a factor of both x^(4)+6x^(2)+25 and 3x^(4)+4x^(4)+28x+5 then the least value of f(x) is 2 b.3 c.5/2 d.4

Let P(x)=x^2+b x+cw h e r eba n dc are integer. If P(x) is a factor of both x^4+6x^2+25a n d3x^4+4x^2+28 x+5,t h e n a.P(x)=0 has imaginary roots b.P(x)=0 has roots of opposite c.P(1)=4 d .P(1)=6

If (x + 6) is a factor of f (x) = x ^(3) + 3x ^(2) + 4x + P, then find the value of P.

If x^(2)+2x-5 is a factor of x^(4)-2x^(3)+px^(2) +qx-35 , then find the value of p^(2)-q .

When (x-a) is a factor of (x^3-3x^2a+2a^2x+p) then find the value of p is:

If (x+2) and (x-2) are factors of ax^4 + 2x - 3x^2 + bx - 4 , then the value of a + b is

Given that x^(2)+x-6 is a factor of 2x^(4)+x^(3)-ax^(2)+bx+a+b-1, find the value of aandb.

NTA MOCK TESTS-JEE MOCK TEST 5-MATHEMATICS
  1. If p , r , s gt 0 then lim(x rarr oo)((p^(1/x)+q^(1/x)+r^(1/x)+s^(1/x)...

    Text Solution

    |

  2. If (27)^999 is divided by 7, then the remainder is .

    Text Solution

    |

  3. If A=[(1,-3), (2,k)] and A^(2) - 4A + 10I = A, then k is equal to

    Text Solution

    |

  4. A piece of cheese is located at (12, 10) in a coordinate plane. A mous...

    Text Solution

    |

  5. Two medians drawn from the acute angles of a right angled triangle i...

    Text Solution

    |

  6. If Z is a non-real complex number, then find the minimum value of (Imz...

    Text Solution

    |

  7. If the coefficient of x^7 in (ax^2+1/(bx))^11 is equal to the coeffici...

    Text Solution

    |

  8. The average of five consecutive odd number is 61. Then the difference ...

    Text Solution

    |

  9. The abscissa of A and B are the roots of the equation x^(2) + 2ax -b^(...

    Text Solution

    |

  10. A tower T(1) of height 60 m is located exactly opposite to a tower T(2...

    Text Solution

    |

  11. The area between the curve y=2x^(4)-x^(2), the x-axis, and the ordinat...

    Text Solution

    |

  12. If a plane, intercepts on the coordinates axes at 8,4,4 then the lengt...

    Text Solution

    |

  13. If f(x) = {{:((sqrt(4+ax)-sqrt(4-ax))/x,-1 le x lt 0),((3x+2)/(x-8), 0...

    Text Solution

    |

  14. Check whether the relation R defined on the set A={1,\ 2,\ 3,\ 4,\ 5,\...

    Text Solution

    |

  15. int(sin^8x-cos^8x)/(1-2sin^2xcos^2x)dx=

    Text Solution

    |

  16. Let p(x) = x^2+bx+c, where b and c are integers. If p(x) is a factor o...

    Text Solution

    |

  17. There are eight rooms on the first floor of a hotel, with four rooms o...

    Text Solution

    |

  18. Let f[1, infty) to [2, infty) be a differentiable function such that f...

    Text Solution

    |

  19. If y = tan^(-1) (sec x - tan x ) , "then" (dy)/(dx) is equal to

    Text Solution

    |

  20. The volume of a cube is increasing at the rate of 18 cm^(3) per secon...

    Text Solution

    |