Explanation for Question 26 From the Math (Calc) Section on the 2020 March Sat
So now we're looking at question number 26, which says that in this quadratic 2 equation here be as a constant. What that means is that B is simply 3 a normal number and it's never going to change is always going to be 4 that same one number. And then we say for what values of B does 5 the quadratic equation only have one solution? 6 And so in order to figure out a number of solutions, 7 right? You have, you can either have one, zero or two solutions. 8 You need to go to the quadratic equation, 9 right? That's X equals opposite B plus or minus 10 square root B squared minus four, 11 AC all over to . 12 And the key for finding out the number of solutions is right here under 13 the radical. And if we're looking under the radical, 14 we're going to hone in on the B squared minus four AC. 15 And so here's going to be a little key for how many solutions you 16 have. 17 If you have one solution, then everything underneath the radicle needs to be equal 18 to zero. If you'd like two solutions, 19 everything under the radical must be positive, 20 right? It must be greater than zero. And now if you want zero solutions, 21 if you want no solutions, everything under the radical must be negative or less 22 than zero. Now, since we want only one solution, 23 that means that we want B squared minus four, AC whatever is under the 24 radical to be equal to zero. 25 And since I'm solving for B, I'll simply plug in my mic and then 26 solve right. A is what's in front of our X, 27 which is going...