polynomials with complex coefficients

An expression of the form in which a i are numbers belonging to some number system and 'n' is a non-negative integer, is called a polynomial. a i are called the coefficients of if a o 0, the polynomial is said to be of degree ..

Which of the following polynomial functions has the leading coefficient 2, degree 3, with - 2, 1 and 4 as real zeros? => f ( x ) = 2 x 3 + 6 x 2 + 12 x + 16 or f ( x ) = 2 x 3 + 6 x 2 - 12 x - 16 or f ( x ) = 2 x 3 - 6 x 2 - 12 x + 16 or f ( x ) = x 3 + x 2 +..

Choose a polynomial function in standard form with real coefficients whose zeros are 2 and - 6 and multiplicity of 3 and 2 respectively. => f(x ) = x 5 + 8 0 x 2 or f(x ) = - 24 x 3 + 8 0 x 2 or f(x ) = x 5 + 6 x 4 + 3 3 6 x - 2 8 8 or f(x ) = x 5 + 6 x 4 - 2 4 x 3 - 8 0 x 2 + 3..

Which of the following is a polynomial of degree 4 with real coefficients that has having zeros 3, - 1, and 2 - i ? => f ( x ) = 2 x 4 - 1 2 x 3 + 2 0 x 2 + 4 x - 30 or f ( x ) = 2 x 4 - 1 2 x 3 - 3 0 x 2 + 4 x - 30 or f ( x ) = 2 x 4 - 1 2 x 3 + 3 0 x 2 + 4 x + 30 or none of th..

Select the polynomial function with leading coefficient 4, degree 4, and zeros - 3, - 1, 0 and 5 2 . => f ( x ) = 4 x 4 + 6 x 3 + 28 x 2 + 30 x or f ( x ) = 4 x 4 + 6 x 3 - 28 x 2 - 60 x or f ( x ) = 4 x 4 + 6 x 3 + 28 or f ( x ) =..

The degree of a polynomial function f ( x ) with real coefficients is 7. Choose the minimum number of real zeros that f ( x ) will have. => 7 or 0 or 6 or 1..

Choose the leading coefficient of the given polynomial function f ( p ) = 11 p - 2 p 2 . => 11 or - 2 or 2 or - 11..

The degree of a polynomial function f ( x ) with real coefficients is 19. Choose the maximum number of nonreal zeros f ( x ) can have. => 17 or 20 or 19 or 18..

Which of the following is true for the polynomial function, f ( x ) having a + ib as a complex zero? => a - ib is also a complex zero of f ( x ) or a + ib is also a complex zero of f ( x ) or - a..

Usually a polynomial is denoted by P(x) and if k is any number then P(k) denotes the value of P(x) at x=k. Then a polynomial can be used to define a function with x or y or any letter of the alphabet. The coefficient of the polynomial may belong to any syste..