Home
Class 12
MATHS
Let p(x) be a polynomial of degree 6 wit...

Let `p(x)` be a polynomial of degree 6 with leading coefficient unity and `p(-x)=p(x)AAxepsilonR`.
Also `(p(1)+3)^(2)+p^(2)(2)+(p(3)-5)^(2)=0` then `sqrt(-4-p(0))` is….

Text Solution

Verified by Experts

The correct Answer is:
6
`[6]`
`p(x)=(x^(2)-4)(x^(4)-10x^(2)+10)`
Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINE

    FIITJEE|Exercise NUMERICAL BASED|4 Videos

  • TIPS

    FIITJEE|Exercise NUERICAL DECIMAL BASED QUATIONS|20 Videos

Similar Questions

Explore conceptually related problems

Let p (x) be a polynomial with real coefficient and p (x)=p'(x) =x^(2)+2x+1. Find P (1).

If P(x) is polynomial of degree 4 with leading coefficient as three such that P(1)=2,P(2)=8,P(3)=18,P(4)=32 then the value of P(5) is

Let p(x) be a polynomial of degree 4 having extremum at x=1,2 and lim_(x rarr0)(1+(p(x))/(x^(2)))=2. Then find the value of p(2)

Let P(x) be a fourth degree polynomial with coefficient of leading term 1 and p(1)=p(2)=p(3)=0, then the value of p(0)+P(4)

Let p(x) be a polynomial of degree 5 having extremum at x=-1,1 and lim_(x rarr0)((P(x))/(x^(3))-1)=7 .The value of |P(2)| is

If p(x) be a polynomial of the lowest degree with integer coefficients such that one of its roots is (sqrt(2)+3sqrt(3)) then |p(1)| is equal to

Let P(x) be a cubic polynomial such that coefficient of x^(3) is 1;p(1)=1,p(2)=2,p(3)=3 then the value of p(4) is :

Let p (x) be a real polynomial of degree 4 having extreme values x=1 and x=2.if lim_(xrarr0) (p(x))/(x^2)=1 , then p(4) is equal to

FIITJEE-TEST PAPERS-MATHEMATICS
  1. sum(m=1)^(oo) sum(n=1)^(oo)(m^(2)n)/(3^(m)(n.3^(m)+m.3^(n)))=p/q (wher...

    Text Solution

    |

  2. If f(x)=sum(r=0)^(20) .^(20)C(r) (In (1+x))^(r),g(x)=sum(r=0)^(20)(-1)...

    Text Solution

    |

  3. Let p(x) be a polynomial of degree 6 with leading coefficient unity an...

    Text Solution

    |

  4. If lim(n->oo)[((2009)^2010)^n+((2010)^2009)^n]^(1/n) is equal to a^b w...

    Text Solution

    |

  5. The value of x, x in (2,oo) where f (x) = sqrt(x sqrt(8x-16))+ sqrt(x-...

    Text Solution

    |

  6. A and B are two square matrices such that A^(2)B=BA and if (AB)^(10)=A...

    Text Solution

    |

  7. Delta I(1)I(2)I(3) is an excentral triangle of an equilateral trian...

    Text Solution

    |

  8. If two points P & Q on the hyperbola ,x^2/a^2-y^2/b^2=1 whose centre i...

    Text Solution

    |

  9. If the equation x^(3)-3x+1=0 has three roos x(1),x(2),x(3) where x(1)l...

    Text Solution

    |

  10. Let S={(x,y),x^(2)+y^(2)-6x-8y+21le0} then "max"{(12x)/7-(5y)/7,(x,y...

    Text Solution

    |

  11. The graph of the derivative f of a continuous function f is shown with...

    Text Solution

    |

  12. If f(x)=int(-2)^(x)(t^(4)-bt^(3)+(b+1)t^(2)-bt+b)dt strictly increases...

    Text Solution

    |

  13. Maximum value of function f(x)=(sin^(-1)(sinx)^(2)-sin^(-1)(sinx) is:

    Text Solution

    |

  14. Consider a parabola x^2-4xy+4y^2-32x+4y+16=0. The focus of the parab...

    Text Solution

    |

  15. Let f(x)=ax^(4)+bx^(2)+3x+7 and f(-4)=2286 and f=(4)=N. The number of ...

    Text Solution

    |

  16. The volume of a right triangular prism ABCA1B1C1 is equal to 3. If the...

    Text Solution

    |

  17. If the equation |z(z+1)^8 =z^8 |z+1| where z in C and z(z+1) != 0 ha...

    Text Solution

    |

  18. If in a /\ABC, a,b,c are in A.P. and P(1),P(2),P(3) are th altitude fr...

    Text Solution

    |

  19. Suppose a(1),a(2),a(3) are in A.P. and b(1),b(2),b(3) are in H.P. and ...

    Text Solution

    |

  20. Given three non-zero, non-coplanar vectors veca, vecb and vecc. vecr1=...

    Text Solution

    |