I have been going through the flash cards and came across this one for EIVs.
Is the statement sufficient?
What are the solutions to the equation x^2 + kx - 10 = 0, where k is a constant?
(1) One of the solutions is -5.
I was able to find the other solution plugging the numbers in.
(x+5) (x-2) since the two numbers in the parentheses need to equal -10 when multiplying.
But I am scratching my head when plugging them into the equation to solve.
you've actually got the more sophisticated solution here, so, nice job.
you can also solve by just plugging -5 in for x, since it's a solution of the equation (according to what you're told). if you plug that number in, you get 25 - 5k - 10 = 0, or 15 - 5k = 0. therefore, k = 3.
this gives you the equation x^2 + 3x - 10 = 0, which can be factored as you've shown above.
the best thing, of course, is to get both
of these solution methods under your belt.