The roots of a quadratic equation are 5 and 2
3
. If one of the two factors of the equation is
x
−
5
, which expression could be a second factor?

2
x
−
3

2 x − − 3

2
x
+
3

2 x + 3

3
x
−
2

3 x − 2

3
x
+
2

3 x + 2

I think before we get to this answer we need to understand how roots of a quadratic equation works.

When a quadratic equation have 2 real roots such as a/b and c/d we can write the quadratic equation in factored form like this y or 0=(bx-a)(dx-c)

In this case we know the 2 roots are 5 and 2/3 and one of the factors is already x-5. so the other one according to the equation above that I wrote have to be 3x-2 and therefore the 3rd choice is correct.

Hope this helped you and if there is any questions about this please let me know in the comments.

logv3(x+2)=1

rewrite in exponential form:

logb(x) = y is equal to b^y =x

b = 3, y = 1

now solve for x:

3^1 = x+2)

x = 3-2

x = 1

see the picture for the graph.

step-by-step explanation: