`ax^(2) + bx + c` is a …………… polynomial.

Let f(x)=ax^(2)+bx+c is a quadratic polynomial if 3a+sqrt(3)b+c=1 and 4a+2b+c=0 then which ofthe following is/are not possible-

Given ax^(2)+bx+c is a quadratic polynomial in x and leaves remainders 6 , 11 and 18 , respectively, when divided by (x+1), (x+2)and(x+3) . Find the value of a + b + c.

(ax^(2) + bx + c)^(n)

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

If the polynomial f(x) = ax^(3) + bx - c is divisible by the polynomial g(x) = x^(2) + bx + c then ab = …………..

If the polynomial f(x)=ax^(3)+bx-c is divisible by the polynomial g(x)=x^(2)+bx+c, then ab=( a) 1 (b) (1)/(c) (c) -1(d)-(1)/(c)

If a gt 0 and discriminant of ax^(2) + 2bx + c is negative, then Delta = |(a,b,ax +b),(b,c,bx +c),(ax +b,bx +c,0)| , is

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 .

Find ax^(p)+bx^(q)+c to be polynomial p & q are:

The polynomial f(x)=ax^(3)+bx-c is divisible by the polynomials g(x)=x^(2)+bx+c,c!=0, if ac=lambda b then determine lambda.