If 4 is a root of x^2- kx+12=0 , then the value of k and the other roots are what?​

k=7

Other root=3

Step-by-step explanation:

If x=4 is a root of the given equation, then it satisfies the given equation.

4^2-k(4)+12=0

We can solve this equation for k.

16-4k+12=0

28-4k=0

28=4k

28/4=k

7=k

So the equation is x^2-7x+12=0

Factor form is (x-3)(x-4)=0 since-3(-4)=12 and -3+-4=-7.

This implies x=3 and x=4 are roots.

guess at question:

a vertical line intersects the graph of g(x,y) = 0 at two points. what conclusion follows about the function f(x) implicitly defined by g(x,f(x)) = 0?

the domain of f(x) cannot include the x coordinate of any such vertical line.

informally, f(x) is not a function, and

g(x,y)=0 cannot be solved for y uniquely.

the relation r = {(x,y) such that g(x,y) = 0} is a function if

for all (a,b) ∊ r and (c,d) ∊ r, a=c implies b=d.

step-by-step explanation: