If `f(x), h(x)` are polynomials of degree 4 and `|(f(x), g(x),h(x)),(a, b, c),(p,q,r)|``=mx^4+nx^3+rx^2+sx+r` be an identity in x, then `|(f'''(0) - f''(0),g'''(0) - g''(0),h'''(0) -h''(0)),(a,b,c),(p,q,r)|` is

If f(x),g(x)a n dh(x) are three polynomial of degree 2, then prove that phi(x)=|f(x)g(x)h(x)f'(x)g'(x h '(x)f' '(x)g' '(x )h ' '(x)| is:

If f(x),g(x),h(x) are polynomials in x of degree 2 and F(x)=|fghf'g' h 'f' 'g' ' h ' '| , then F^(prime)(x) is equal to 1 (b) 0 (c) -1 (d) f(x)dotg(x)doth(x)

If f(x),g(x)a n dh(x) are three polynomial of degree 2, then prove that "phi(x)=|{:(f(x),g(x),h(x)),(f'(x),g'(x),h'(x)),(f''(x),g''(x),h''(x)):}| is a constant polynomial.

If f(x) g(x) and h(x) are three polynomials of degree 2 and Delta = |( f(x), g(x), h(x)), (f'(x), g'(x), h'(x)), (f''(x), g''(x), h''(x))| then Delta(x) is a polynomial of degree (dashes denote the differentiation).

If f(x), g(x), h(x) are polynomials of three degree, then phi(x)=|(f'(x),g'(x),h'(x)), (f''(x),g''(x),h''(x)), (f'''(x),g'''(x),h'''(x))| is a polynomial of degree (where f^n (x) represents nth derivative of f(x))

If h(x)= f(f(x)) for all x in R, and f(x)= x^3 + 3x+2 , then h(0) equals

If f(x) and g(x) are of degrees 7 and 4 respectively such that f(x)= g(x) q(x)+ r(x) then find possible degrees of q(x) and r(x) .

If f(x),g(x) and h(x) are three polynomials of degree 2, then prove that phi(x) = |[f(x),g(x),h(x)],[f ^ (prime)(x),g^(prime)(x),h^(prime)(x)],[f^(primeprime)(x),g^(primeprime)(x),h^(primeprime)(x)]| is a constant polynomial.

If f(x) and g(x) are two polynomials such that the polynomial h(x)=xf(x^3)+x^2g(x^6) is divisible by x^2+x+1, then f(1)=g(1) (b) f(1)=1g(1) h(1)=0 (d) all of these

If f_(r)(x), g_(r)(x), h_(r) (x), r=1, 2, 3 are polynomials in x such that f_(r)(a) = g_(r)(a) = h_(r) (a), r=1, 2, 3 and " "F(x) =|{:(f_(1)(x)" "f_(2)(x)" "f_(3)(x)),(g_(1)(x)" "g_(2)(x)" "g_(3)(x)),(h_(1)(x)" "h_(2)(x)" "h_(3)(x)):}| then F'(x) at x = a is ..... .