Let` f(x) = x^4 + ax^3 + bx^2 + cx + d` be a polynomial with real coefficients and real roots. If |f(i)|=1where `i=sqrt(-1)`, then the value of a +b+c+d is

Let f(x)=x^(3)+ax^(2)+bx+c be a cubic polynomial with real coefficients and all real roots.Also |f(iota|=1 where iota=sqrt(-1) statement-1: All 3roots of f(x)=0 are zero Statement-2: a+b+c=0

Let f(x)=ax^(3)+bx^(2)+cx+d be a cubic polynomial with real coefficients satisfying f(i)=0 and f(1+i)=5. Find the value of a^(2)+b^(2)+c^(2)+d^(2)

Let f (x) =x ^(2) + ax +b and g (x) =x ^(2) +cx+d be two quadratic polynomials with real coefficients and satisfy ac =2 (b+d). Then which of the following is (are) correct ?

Let f (x) =x ^(2) + ax +b and g (x) =x ^(2) +cx+d be two quadratic polynomials with real coefficients and satisfy ac =2 (b+d). Then which of the following is (are) correct ?

Let P(x)=x^3+ax^2+bx+c be a polynomial with real coefficients, c!=0andx_1,x_2,x_3 be the roots of P(x) . Determine the polynomial Q(x) whose roots are 1/x_1,1/x_2,1/x_3 .

If f (x)= 0 be a polynomial whose coefficients are all +-1 and whose roots are all real, then degree of f (x) can be : (a) 1 (b) 2 (c) 3 (d) 4

The polynomial f(x)=x^(4)+ax^(3)+bx^(3)+cx+d has real coefficients and f(2i)=f(2+i)=0. Find the value of (a+b+c+d)

Let f(x) be a polynomial with real coefficients such that f(0)=1 and for all x ,f(x)f(2x^(2))=f(2x^(3)+x) The number of real roots of f(x) is:

The polynomial f(x)=x^4+a x^3+b x^3+c x+d has real coefficients and f(2i)=f(2+i)=0. Find the value of (a+b+c+d)dot