The Discriminant - Problem 1
This problem asked me to find out how many solutions there are. It doesn’t ask me to find out what the values are, it just asks me how many there are. So that tells me I’m going to be using the discriminant.
The formula for the discriminant is b² minus 4ac and if that’s positive, I'm goinng to have two solutions, if it’s negative; I’m going to have no solutions. I’m abbreviating ‘solutions’ and if it's zero I’m going to have one solution.
That’s something you just need to memorize or maybe keep in your notes, apostrophes are in the wrong place, okay there we go. That's something you need to memorize or keep in your notes that you have at handy when you’re doing these problems. So the letters a, b and c are the coefficients of my trinomial in standard form. But this guy is not in standard form yet, I have to set it equal to zero so I'll have 3x² minus 2x minus 7 equals zero. A is equal to 3, b is equal to -2 and c is equal to -7.
Let’s plug it into this formula and see if we get positive, negative or equal to zero. Here we go. B² is going to be -2² minus 4 times my a value times my c value. If I do that out I’ll get 4 plus 12 times 7 is 84, so I’ll have 88. Doesn’t matter exactly what this value is, it’s okay if you do the multiplying wrong, as long as you notice that you get a positive discriminant.
Positive discriminant means that there’s 2 solutions, that’s the answer to my problems. It said find the number of solutions, I know there are two solutions. If it’d ask me to find those solutions then I’d have to use one of my other strategies like completing the square, quadratic formula, factoring, blah, blah, blah. It just asked me here how many there were so I’m all done.