If 4 is a root of x^2+kx-48=0, find the other root and the value of k.

Question

cwrw238 · Answer

(x - 4)(x + 12) = x^2 + 8x - 48
so compare this to x^2 + kx - 48 = 0  to find k

cwrw238 · Answer

understand?

anonymous · Answer

But where did you find the values x+12 and k?

cwrw238 · Answer

4 is a given root so one factor of the trinomial x^2 + kx - 48  must be (x - 4)
and in order to get the -48  the other factor must be (x + 12)

cwrw238 · Answer

expanding (x-4)(x+12)  gives x^2 + 12x - 4x - 48 = x^2 + 8x - 48

cwrw238 · Answer

now if we compare this with the original equation:

x^2 + 8x - 48 = 0
x^2 + kx - 48 = 0

comparing 8x and kx:  k must be 8

cwrw238 · Answer

and other root is -12

cwrw238 · Answer

plz ask if you need more explanation

anonymous · Answer

Oh. Is there another method?

cwrw238 · Answer

there could be but the above method is ok - i was really asking if you understood it

anonymous · Answer

I did. But it was more speculation than mathematical method.

cwrw238 · Answer

not speculation at all

anonymous · Answer

To factor, the factors of the constant term have to add to the linear term.  Given that x=4 is a root, (x-4) has to be a factor.  Therefore, in order to get the -48 constant term, (x+12) needs to be the other factor.  This will give k = 8 when you evaluate the product.