00:01
In this question, we are given a quadratic polynomial and we are told that one of the roots of the polynomial is 5 halves.
00:08
And we are asked to find the other root.
00:11
Now, recall that every polynomial, every quadratic polynomial could be factored as 2, the coefficient in front of x squared, times x minus 1 root, times x minus the other root, let's call it x2.
00:30
And we're going to write this by foiling as 2x squared.
00:35
Well, let's do it step by step as 2 times x squared minus 5 half x, minus x 2 times x and plus 5 halves times x2.
00:52
Now, and we can write this as 2x squared minus 5x minus 2x2x plus 5x2.
01:08
And by factoring out x we are going to get 2x squared.
01:12
Minus 5 plus 2x2 times x plus 5x2.
01:22
Now let's compare this to the left hand side...