Functions question

Question

f(x)= x²+6x+8

A(-4,0)

B(-2,0)

C(0,8)

what is the relationship between the value of c and the roots of f(X)?

 

is there a relationship between the roots and the coefficient Of X? Explain your answer 

 

Answer 1

f(x) can be written = (x+4) (x+2). Using this, we see that the roots are (-2) and (-4). In one sense there is a relationship between the value of C and the roots of f(x). If I set f(x) = 0 and write f(x) = x² + 6x + (C), then the roots of f(x) are:

 

[-6 +- [36- 4C]^1/2]/4

 

As to the second question, is there a relationship between the roots and the coefficient of the linear power of (x), which for f(x) is 6, the answer as shown above is again yes.