Tip:
Highlight text to annotate it
X
For a good time, solve this shmoopy question… Solve for y: 2y squared plus 7y plus 3 equals
zero. And here are the potential answers…
OK so what is this question asking?
It’s just a basic factoring question. It’s in the form of something squared plus something
plus an integer equals zero.
A bell should be going off when we see an equation like this… and we should either
recognize the form, or suddenly and unexplainably want to eat dog food.
We just have to figure out what the factors are… and there’s a bit of a curveball
here in that there’s a 2 on the front end.
So we know that one of the factors is going to be a 2, as in:
The quantity 2y plus something times the quantity y plus something.
Let’s plug in some numbers to get the 3. It’s kind of easy because 3 only has 2 factors:
1 and 3…
…so it’s really high odds – especially in problems like these where they don’t
want messy numbers – that the answer is going to be 1 and 3. Clean.
Now we have quantity 2y plus 1 times quantity 2y plus 3… and aha! If we multiply it out, we get 2y times y here, which is 2y squared. Check.
Then we have outside times outside plus inside times inside… or 2y times 3, which is 6y
plus y times 1, which is just… y.
Our total is 7y; then, 1 times 3 is just 3 so we’re done.
But now… how do we make the whole thing equal to zero? Well, one of the elements here
has to BE zero.
If y is negative 3 then this one is 3 minus 3 which is 0…
…and here, it’s just negative one half, because negative 1 half times 2 is negative
1… and negative 1 plus positive 1 is zero.
So the other answer is negative one half and the answer is A and C…
…or option E.
Uh-oh… was that the dinner bell?