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`

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)

Given that the zeros of the cubic polynomial f(x) = x^3 -6 x^2 + 3x + 10 are a, a+b, a + 2b for some real number a and b. Find the values of a and b as well as the zeros of the given polynomial.

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

A nonzero polynomial with real coefficient has the property that f(x)=f'(x)f(x) .If a is the leading coefficient of f(x), then the value of (1)/(2a) is

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:

f(x) is a cubic polynomial x^(3)+ax^(2)+bx+c such that f(x)=0 has three distinct integral roots and f(g(x))=0 does not have real roots,where g(x)=x^(2)+2x-5, the minimum value of a+b+c is

A nonzero polynomial with real coefficients has the property that f(x)=f'(x)cdotf''(x). If a is the leading coefficient of f(x), then the value of 1//a is -

If x=2 and x=0 are roots ofthe polynomial f(x)=2x^(3)-5x^(2)+ax+b. Find the values of a and b

If x=2 and x=0 are roots of the polynomial f(x)=2x^(3)-5x^(2)+az+b. Find the values of a and b.