sum and product of roots, how do you do it!?

Question

it says find k

x^2 + kx - 39 = 0: r1=3


*r1, the 1 is small and is under the r to the bottom right

Answer 1

(x - 3)(x + 13)
x^2 + 13x - 3x - 39
x^2 + 10x - 39

k = 10

Answer 2

Solution:

Since r1 = 3, it follows that one of the factors is (x - 3)

So the factors will look like:

(x - 3) (x + 13) = 0

Expanding this equation, we get:

(x - 3)*x + (x-3)*13 = 0
x^2 -3x + 13x - 39 = 0
x^2 + 10x - 39 = 0

So k = 10

Answer 3

r_1 is one of the roots.

the sum of the roots is the coefficient of the second largest power in the variable over the leading coefficient:

k/1 = k -> doesnt help us a lot

the product of the roots for an even degree is the constant over the leading coefficient:

-39/1 ->-39

to find the sum simply divide the factor (x-3) into your quadratic, then add the root you get to 3.