Given that the function f (x) = x ^ 4 + ax ^ 3 + 2x ^ 2 + B, XAB belongs to R. if the function f (x) has an extreme value only at x = 0, find the value range of A Who can help me explain why the derivative function is obviously not a root when x = 0?

Given that the function f (x) = x ^ 4 + ax ^ 3 + 2x ^ 2 + B, XAB belongs to R. if the function f (x) has an extreme value only at x = 0, find the value range of A Who can help me explain why the derivative function is obviously not a root when x = 0?

2009-10-20 17:56 f(x)=x^4+ax^3+2x^2+b,f'(x)=4x^3+3ax^2+4x
Let f '(x) = 0, that is, 4x ^ 3 + 3ax ^ 2 + 4x = 0, X (4x ^ 2 + 3ax + 4) = 0,
It can be seen from the condition that only x = 0, that is, 4x ^ 2 + 3ax + 4 is not equal to 0,
That is, the discriminant △ = 9A ^ 2-64

The function f (x) = x ^ 4 + AX3 + 2x2 + B, if the function f (x) has an extreme value only at x = 0, the value range of a is obtained
Why wait

f(x)=x^4+ax^3+2x^2+b,
f'(x)=4x^3+3ax^2+4x
=x(4x^2+3ax+4),
F (x) has an extreme value only at x = 0,
The equation 4x ^ 2 + 3ax + 4 = 0 of X has no real root,
∴（3a)^2-4*4*4