Define a polynomial with real coefficients.

Write the standard form of a linear polynomial with real coefficients.

Write the standard form of a cubic polynomial with real coefficients.

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:

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

For a polynomia g(x) with real coefficients, let m_(g) denote the number of distinct real roots of g(x). Suppose S is the set of polynomials with real coefficients defined by S={(x^(2)-1)^(2)(a_(0)+a_(1)+a_(2)x^(2)+a_(3)x^(3)): a_(0) a_(1), a_(2), a_(3)= RR} For a polynomial f. let f and f denote its first and second order derivties, respectively. Then the minimum possible value of (m_(f')+m_(f")) . where f in S is, ____

Write the standard form of a quadratic polynomial with real coefficients.

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

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 -

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