Question

One of the roots of the equation
x^2+Kx−6=0
is 3 and K is a constant.

Which one is greater

a. The value of K

b. -1

Answer 1

one of the roots is 3
that means
x=3
or , adding -3 to both sides, x-3=0

let the other root be called "a"
then we know
(x-3)(x-a)=0
multiply that out
x^2 -3x-ax +3a = 0
or
x^2 -(3+a) x + 3a =0

Answer 2

match up
x^2 -(3+a) x + 3a =0
x^2+Kx−6=0

we see 3a= -6
solve for a by dividing both sides by 3
we get
a= -2

Answer 3

using a= -2 in
x^2 -(3+a) x + 3a =0
x^2 -(3-2) x +3*-2 = 0

simplifying:
x^2 - (1) x -6 =0 or
x^2 -x -6 =0

Answer 4

it looks like K= -1

Answer 5

why is one of the roots 3?

Answer 6

It says
One of the roots of the equation x^2+Kx−6=0 is 3

Answer 7

Hey how do i know if it's (x-3)(x-a) and not (x+a) ?????????

Answer 8

I tried (x-3)(+a) and it worked out better

Answer 9

(x+a)*

Answer 10

say you factored a quadratic and got
(x-3)(x-2) = 0
the roots are the x values that make this expression zero.
this will be zero if x=3 (which makes 3-3 zero) or x=2 (which makes 2-2 zero)

if you had
(x-3) (x+2)=0
the second root is when x= -2
notice if we write (x+2) as (x - (-2))
the number -2 is the root.

in other words, if we write (x-a) then a will be the root (the x value that makes the expression zero)

Answer 11

btw, what is question ? It looks like it was cut off at the top.

Answer 12

It's asking which one is greater a or b

Answer 13

so in what cases would it be (x-3) (x+a)

Answer 14

in this case , K = -1, so they are equal

Answer 15

I'm still having a hard time understanding how I would know for sure that it would be (-)(-) instead of (-)(+) or (+)(-)

Answer 16

Let's factor x^2 -x -6 =0
the -6 means 1) different signs on the roots, 2) they multiply to give us 6
1,6
2,3
are the choices

the -1x means the larger nuumber is negative, and they add to -1
so
2 and -3 are the factors
(x+2)(x-3)=0
or
(x - (-2)) (x-3) = 0

Answer 17

I guess the point is you can always write the factors
as
(x - a)
where a is the root.
if the root were -2
x= -2 makes the expression zero, then
the factor would be (x- -2) (which is the same as (x+2) )

Answer 18

But I think I am being a clear as mud here.

Answer 19

lolol