00:03
The question here is, can a quadratic equation have two solutions, one of which is not actually a solution? if two solutions are found and one does not check, then does that mean there are no solutions true or false? example number three in the textbook actually is a good example that shows that this is false.
00:32
There can be one extraneous solution.
00:35
I rewrite this by isolating the radical and then squaring everything, and combining like terms so that i have quadratic expression.
00:47
When i factor it and solve it, i get two solutions x equals negative 11 over 4, and x equals negative 2.
00:58
So these are the two solutions that i find doing the algebra.
01:11
But if i plug negative 11 over 4 back in for x, i will get 4 times negative 11 over 4, which actually i'm going to do this a little more quickly.
01:30
I'm going to get negative 11 minus the square root of negative 11 over 4 plus 3 equals negative 10.
01:49
That's negative 11 minus the square root of 112 equals negative 10.
02:04
Negative 11 plus 1 would give me negative 10.
02:09
There is no way that i can subtract a positive value from negative 11 and get a negative 10...