yumi2012 wrote:What are the roots of x²+kx-10

(1) one of the roots is -5

If one root is -5, we know one of the factors of the quadratic expression is (x+5). We now know the other factor is (x-2)...

It's important to recognize that your question is incomplete.
x² + kx - 10 cannot have any roots (solutions), because x² + kx - 10 is not an equation.
For example, we cannot ask someone to "solve" 2x + 5, but we can ask someone to solve 2x + 5 = 11

I'm going to assume that the original question says . . .

What are the roots of x² + kx - 10 = 0

(1) one of the roots is -5

Statement 1: one of the roots is -5

If one of the roots is -5, then x = -5 is a solution to the equation.
So, we can not plug x = -5 into the equation to get: (-5)² + k(-5) - 10 = 0
Simplify: 25 - 5k - 10 = 0
Simplify: 15 - 5k = 0
Solve: k = 3

So, the equation is x² + 3x - 10 = 0
Now that we know the equation, we can definitely find its roots (of course, we don't need to actually find the roots. We need only determine that we could find them)
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Cheers,
Brent

If you're interested, I created a similar (but SUPER HARD) question for BTG a few years ago: https://www.beatthegmat.com/mba/2010/09/ ... er-13-2010

Cheers,
Brent

I'm not entirely sure I agree with you, Matt (although I could be wrong)

From the Official Guide:
The solutions of an equation are also called the roots of the equation. These roots can be checked by substituting them into the original equation to determine whether they satisfy the equation

Asking test-takers to find the root of an expression (like 3x) seems too ambiguous for the GMAT. Are there some specific (official) questions you're thinking of?

Cheers,
Brent