Explanation for Question 27 From the Math (Calc) Section on the 2020 October Sat
So question 27 is asking us what must be true about the variable B 2 if we want to have no solution to this equation, 3 this quadratic equation. So something that's really useful to know about these quadratic equations 4 is how, you know, how many solutions are possible. 5 And we do that by looking here at the quadratic formula and looking specifically 6 at what is under the radical. 7 And so if we look at what's under the radical, whatever is here, 8 whatever number is underneath this, if it's zero, 9 then you have one solution. If that number is positive, 10 you have two solutions. Now, if the number under here is negative, 11 you have zero solutions. And that should make sense because you can't square root 12 a negative number. So if you have a negative number underneath the radical, 13 you don't have any answers. And now we're looking for no real solutions, 14 which is the same as zero solutions. 15 So we want B squared minus four AC to be less 16 than zero. And lucky enough for us, 17 we know what a and C are and we can get it from this 18 equation, right? So B squared minus four times three, 19 which is our, a times five, 20 which is our C is less than zero. 21 Now, if I multiply all this out, I get 60. 22 So B squared minus 60 is less than zero. 23 I can add 60 to both sides to solve for B squared. 24 And I get B squared is less than 60, 25 which leads me to choose answer choice a.