Home
Class 12
MATHS
Let p (x) be a polynomial with real coef...

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

Text Solution

Verified by Experts

The correct Answer is:
2
Promotional Banner

Topper's Solved these Questions

  • QUADRATIC EQUATIONS

    VK JAISWAL ENGLISH|Exercise EXERCISE (MATCHING TYPE PROBLEMS)|3 Videos

  • PROBABILITY

    VK JAISWAL ENGLISH|Exercise Exercise -5 : Subjective Type problems|11 Videos

  • SEQUENCE AND SERIES

    VK JAISWAL ENGLISH|Exercise EXERCISE (SUBJECTIVE TYPE PROBLEMS)|21 Videos

Similar Questions

Explore conceptually related problems

Let P(x) be a polynomial with real coefficients such that P(sin^2x) = P(cos^2x) , for all xϵ[0,π/2] . Consider the following statements: I. P(x) is an even function . II. P(x) can be expressed as a polynomial in (2x−1) 2 III. P(x) is a polynomial of even degree . Then

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….

Let P(x) =x^(2)+ 1/2x + b and Q(x) = x^(2) + cx + d be two polynomials with real coefficients such that P(x) Q(x) = Q(P(x)) for all real x. Find all the real roots of P(Q(x)) =0.

Let P(x) = x^10+ a_2x^8 + a_3 x^6+ a_4 x^4 + a_5x^2 be a polynomial with real coefficients. If P(1)=1 and P(2)=-5 , then the minimum-number of distinct real zeroes of P(x) is

Let P(x) be quadratic polynomical with real coefficient such tht for all real x the relation 2(1 + P(x)) = P(x - 1) + P(x + 1) holds. If P(0) = 8 and P(2) = 32 then Sum of all coefficients of P(x) can not be

Let P(x) be quadratic polynomical with real coefficient such tht for all real x(1) the relation 2(1 + P(x)) = P(x - 1) + P(x + 1) holds. If P(0) = 8 and P(2) = 32 then If the range of P(x) is [m, oo) then 'm' is less then

P(x) is said to be a monic polynomial if its leading coefficient is 1. If P(x) is divided b (x-a) the remainder is given by P(a). If P(a) = 0 then (x-a) is called factor of P(x). If P(x) is a monic polynomial of degree 4 such that P(1) = P(2) = P(3) = P(4) = 2. The value of P(0) is

P(x) is said to be a monic polynomial if its leading coefficient is 1. If P(x) is divided b (x-a) the remainder is given by P(a). If P(a) = 0 then (x-a) is called factor of P(x). If P(x) is a monic polynomial of degree 4 such that P(1) = P(2) = P(3) = P(4) = 2. The value of P(5) is

Determine all polynomial p(x) with rational coefficient so that for all x with |x|le1 , p(x)=p((-x+sqrt(3-3x^(2)))/(2)) .

Let P(x) = x^(2) + ax + b be a quadratic polynomial with real coefficients. Suppose there are real numbers s ne t such that P(s) = t and P(t) = s. Prove that b - st is a root of the equation x^(2) + ax + b st =0 .

VK JAISWAL ENGLISH-QUADRATIC EQUATIONS -EXERCISE (SUBJECTIVE TYPE PROBLEMS)
  1. Let p(x)=0 be a polynomial equation of the least possible degree, with...

    Text Solution

    |

  2. The range of value's of k for which the equation 2 cos^(4) x - sin^(4...

    Text Solution

    |

  3. Let p (x) be a polynomial with real coefficient and p (x)-p'(x) =x^(2)...

    Text Solution

    |

  4. Find the smallest positive integral value of a for which the greater r...

    Text Solution

    |

  5. If the equation x ^(4)+kx ^(2) +k=0 has exactly two distinct real root...

    Text Solution

    |

  6. Let a,b,c, d be the roots of x ^(4) -x ^(3)-x ^(2) -1=0. Also consider...

    Text Solution

    |

  7. The number of integral value of a,a, in [-5, 5] for which the equation...

    Text Solution

    |

  8. The number of non-negative integral vlaues of n, n le 10 so that a roo...

    Text Solution

    |

  9. If and y ar real numbers connected by the equation 9x ^(2)+2xy+y^(2) -...

    Text Solution

    |

  10. Consider two numbers a,b, sum of which is 3 and the sum of their cubes...

    Text Solution

    |

  11. If y ^(2)(y^(2) -6) + x ^(2) -8x +24 =0 and the minimum value of x ^(...

    Text Solution

    |

  12. Consider the equation x ^(3) -ax ^(2) +bx-c=0, where a,b,c are ration...

    Text Solution

    |

  13. Let alpha satisfy the equation x ^(3) +3x ^(2) +4x+5=0 and beta satisf...

    Text Solution

    |

  14. The number of ordered pairs (a,b) where a,b are integers satisfying th...

    Text Solution

    |

  15. The real value of x satisfying ""^(3)sqrt(20x +^(3)sqrt(20x+13))=13 c...

    Text Solution

    |

  16. If the range of the values of a for which the roots of the equation x ...

    Text Solution

    |

  17. Find the number of positive integers satisfying the inequality x^(2) -...

    Text Solution

    |

  18. If sin theta and cos theta are the roots of the quadratic equation ax...

    Text Solution

    |

  19. Let the inequality sin ^(2) x+a cos x +a ^(2) ge1+ cos x is satisfied...

    Text Solution

    |

  20. If alpha,beta are the roots of the equation 2x^2-35+2=0 , the find the...

    Text Solution

    |