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:
`P(1)=4`
Promotional Banner

Topper's Solved these Questions

  • QUADRATIC EQUATION

    MOTION|Exercise EXERCISE 4 (PREVIOUS YEAR| JEE MAIN)|25 Videos

  • QUADRATIC EQUATION

    MOTION|Exercise EXERCISE -2 (MCQ)|9 Videos

  • PERMUTATION AND COMBINATION

    MOTION|Exercise EXAMPLE|23 Videos

  • SEQUENCE & SERIES

    MOTION|Exercise Exercise -4 Level -II Previous Year /JEE Advanced|22 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.

MOTION-QUADRATIC EQUATION-EXERCISE -3 (SUBJECTIVE)
  1. Suppose a cubic polynomial f(x) = x^3 + px^2 + qx + 72 is divisible by...

    Text Solution

    |

  2. If g(x)=x^(3)+px^(2)+qx+r where p,q,r are integers. If g(0) and g(-1)...

    Text Solution

    |

  3. If x be real then find the range of the following rational expressions...

    Text Solution

    |

  4. Find the values of k for which |(x^2+k x+1)/(x^2+x+1)|<2,AAx in R

    Text Solution

    |

  5. Find the range of values of a, such that f(x)=(ax^2+2(a+1)x+9a+4)/(x^2...

    Text Solution

    |

  6. The least value of the quadratic polynomial, f(x) = (2p^(2) + 1) x^(2)...

    Text Solution

    |

  7. Find all real numbers x such that (x-1/x)^(1/2)+(1-1/x)^(1/2)=x

    Text Solution

    |

  8. The minimum value of ((x+1/x)^6-(x^6+1/(x^6))- 2)/((x+1/x)^3+x^3+1/x^...

    Text Solution

    |

  9. Find the product of the real roots of the equation, x^2+18x +30=2sqrt(...

    Text Solution

    |

  10. The values of b for which the equation 2log(1/25)(bx+28)=1log5(12-4x-x...

    Text Solution

    |

  11. Find all the values of the parameters c for which the inequality has a...

    Text Solution

    |

  12. Find the complete set of real values of a for which both roots of the ...

    Text Solution

    |

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

    Text Solution

    |

  14. Find the value of k for which one root of the equation of x^(2)-(k+1)x...

    Text Solution

    |

  15. If the roots of x^2-ax+b=0 are real and differ by a quantity which is ...

    Text Solution

    |

  16. If alpha, beta are the roots of the equation x^(2)-2x-a^(2)+1=0 and ga...

    Text Solution

    |

  17. Find the values of k so that the quadratic equation x^2+2(k-1)x+k+5=0 ...

    Text Solution

    |

  18. If the equation has four real and distinct roots, then lamda lies in t...

    Text Solution

    |

  19. If the equation has four real and distinct roots, then lamda lies in t...

    Text Solution

    |

  20. If the equation has only two real roods, then the set of values of lam...

    Text Solution

    |