If `f(x)=x^3+b x^2+c x+d` and `0

If f(x)=x^3+b x^2+c x+d and f(0),f(-1) are odd integers, prove that f(x)=0 cannot have all integral roots.

If f(x)=x^3+b x^2+c x+d and f(0),f(-1) are odd integers, prove that f(x)=0 cannot have all integral roots.

If f(x) = x^(3) + bx^(2) + cx + d and 0 lt b^(2) lt c , then in (-oo, oo) , a)f(x) is a strictly increasing function b)f(x) has local maxima c)f(x) is a strictly decreasing function d)f(x) is bounded

Let f(x)=a x^3+b x^2+c x+d , a!=0 If x_1 and x_2 are the real and distinct roots of f prime(x)=0 then f(x)=0 will have three real and distinct roots if

If the zeros of the polynomial f(x)=a x^3+3b x^2+3c x+d are in A.P., prove that 2b^3-3a b c+a^2d=0 .

If f(x)=x^3+2x^2+3x+4 and g(x) is the inverse of f(x) then g^(prime)(4) is equal to- 1/4 (b) 0 (c) 1/3 (d) 4

If f(x)=x^3+2x^2+3x+4 and g(x) is the inverse of f(x) then g^(prime)(4) is equal to- 1/4 (b) 0 (c) 1/3 (d) 4

If f(x)=x^(3)+2x^(2)+3x+4 and g(x) is the inverse of f(x) then g'(4) is equal to a.(1)/(4) b.0 c.(1)/(3) d.4

If f(x)=x^(3)+2x^(2)+3x+4 and g(x) is the inverse of f(x) then g'(4) is equal to- (1)/(4)(b)0 (c) (1)/(3)(d)4

Let f(x)=ax^2-bx+c^2, b != 0 and f(x) != 0 for all x ∈ R . Then (a) a+c^2 2b (c) a-3b+c^2 < 0 (d) none of these