just for my understanding, can k=1, as 2 squared +2*1 -6=0? Somebody pls help .

Could you please elaborate better what do you mean.

It is not that clear.

Regards

No, k cannot equal 1, because we are told that k is a constant, meaning it's value does not change.

We know that 3 is a root, so when x = 3, the equation works. When x = 3, then k = -1. This means that k is -1, period. It cannot be anything different.

Your equation requires x = 2 and k = 1, but we know this is wrong, because k is not 1, it is -1. We can change the value of x, but not of k.

it can solved in the head

if you solve the equation after you substitute 3 for x how do you get -1
9+3k-6=0
-9 -9
3k-15=0
+15+15
3k=15
/3 /3
k=5
or
9+3k-6=0
+6 +6
15+3k=0
-15 -15
3k=-15
/3 /3
k=-5

It says that ONE of the roots is 3. Isnt it possible tu plug -3 instead of 3?
This would give you two different results, making D the correct choice.

No

If one of the roots is 3 then we do have x-3=0 which means that x=3

Hope this helps

Solution:

We are given that x^2 + kx - 6 = 0, and that one of the roots is 3, and that k is constant.

We need to determine whether k is greater than -1.

Since one of the roots is 3, x = 3. Now we can determine k:

3^2 + k(3) - 6 = 0

9 + 3k = 6

3k = -3

k = -1

Quantity A equals Quantity B.

Answer: C

Hi Brent GreenlightTestPrep
x^2+kx-6=0 is 3
If I had use FOIL, I got (x+3)(x-2) due to k is positive here therefore I make 3 as positive
but then I will get x=-3 or x=2, which doesn't match with the given condition of one the root is 3.
Where has the reasoning gone wrong here or we should ignore +/- sign in the given x^2+kx-6=0 here ?
Could you help clarify? Thanks

How do you know k is positive?
Just because there isn't a "-" in front of k, doesn't mean k is positive.

For example, in the equation k + 3 = 1, k APPEARS to be positive, but when we solve the equation, we get k = -2.

Make sense now thanks Brent GreenlightTestPrep
Will need to ignore the +/- sign in the given formula.