Let `f(x) = x^3 + ax^2 + bx + c` where `a, b,c in R`, then which of the following statement(s) is/are correct?

Consider the cubic equation x^(3)+ax^(2)+bx+c=0, where a,b,c are real numbers,which of the following statements is correct?

If f(x) = ax^(2) + bx + c , where a ne 0, b ,c in R , then which of the following conditions implies that f(x) has real roots?

Let f(x) = ax^(3) + bx^(2) + cx + d, a != 0 , where a, b, c, d in R . If f(x) is one-one and onto, then which of the following is correct ?

Let f(x) = ax^(3) + bx^(2) + cx + d, a != 0 , where a, b, c, d in R . If f(x) is one-one and onto, then which of the following is correct ?

Let f(x) = ax^(3) + bx +c . Then when f is odd,

Let f(x) = a x^2 + bx + c , where a, b, c in R, a!=0 . Suppose |f(x)| leq1, x in [0,1] , then

Let f(x) = a x^2 + bx + c , where a, b, c in R, a!=0 . Suppose |f(x)| leq1, x in [0,1] , then

Let f(x) = a x^2 + bx + c , where a, b, c in R, a!=0 . Suppose |f(x)| leq1, x in [0,1] , then

Let f(x) = a x^2 + bx + c , where a, b, c in R, a!=0 . Suppose |f(x)| leq1, x in [0,1] , then

Let f (x) be a polynomial function of degree 3 where a lt b lt c and f (a) =f (b) = f(c ). If the graph of f (x) is as shown, which of the following statements are INCORRECT ? (Where c gt|a|)