Question

One solution of the equation 2x2 − x − 10 = 0 is five over two. What is the other solution?

Answer 1

-2

Answer 2

if one solution is
\[\frac{5}{2}\] then you know
\[2x^2-x-10=(2x-5)(x+2)\]

Answer 3

If you start with 2x2 − x − 10 = 0 and divide everything by 2 to make the leading coefficient 1, you get x^2-(1/2)x-5 = 0

Now it turns out that for something like x^2+bx+c = 0, the two roots/solutions p and q multiply to the last coefficient c. In other words, pq = c


Since one root is 5/2, we know that (5/2)q = -5


Now solve for q to get q = -10/5 = -2


So the other root is -2