Let `f(x)=x^(3)+ax^(2)+bx+c` be the given cubic polynomial and `f(x)=0` be the corresponding cubic equation, where `a, b, c in R.` Now, `f'(x)=3x^(2)+2ax+b`
Let `D=4a^(2)-12b=4(a^(2)-3b)` be the discriminant of the equation `f'(x)=0`.
IF `D=4(a^(2)-3b)lt0`. Then,

Let f(x)=x^(3)+ax^(2)+bx+c be the given cubic polynomial and f(x)=0 be the corresponding cubic equation, where a, b, c in R. Now, f'(x)=3x^(2)+2ax+b Let D=4a^(2)-12b=4(a^(2)-3b) be the discriminant of the equation f'(x)=0 . If D=4(a^(2)-3b)gt0 and f(x_(1)).f(x_(2))gt0 where x_(1),x_(2) are the roots of f'(x), then

Let f(x) = ax^(2) - bx + c^(2), b ne 0 and f(x) ne 0 for all x in R . Then

If f(x)=x^3+bx^2+cx+d and 0< b^2 < c , then

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For f(x)=x^(3)+bx^(2)+cx+d , if b^(2) gt 4c gt 0 and b, c, d in R , then f(x)

If 1,2,3 and 4 are the roots of the equation x^4 + ax^3 + bx^2 +cx +d=0 then a+ 2b +c=

If f(x) =ax^(2) + bx + c satisfies the identity f(x+1) -f(x)= 8x+ 3 for all x in R Then (a,b)=

Let f(x)=a+b|x|+c|x|^(2) , where a,b,c are real constants. The, f'(0) exists if

Let f(x)=a^2+b x+c where a ,b , c in R and a!=0. It is known that f(5)=-3f(2) and that 3 is a root of f(x)=0. Then find the other of f(x)=0.

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