Explanation for Question 28 From the Math (Calc) Section on the 2020 March Sat
So let's take a look at number 28, which says that in the equations 2 above a and B are positive constants in a is not equal to B. 3 So when it says positive Constance, all it means is that they're positive numbers 4 and they're never going to change. So a will always be the same number 5 and B will also always be the same number they're constant. 6 Right? And then it asks us how many distinct X intercepts does 7 the graph of this equation have in the X, 8 Y plane. So now when we think about X intercepts, 9 right, that's a spot where we cross the X axis. 10 So for example, and the crazy graph that I just drew, 11 we cross the X axis at 1, 2, 3, 4, 5, 6 spots, 12 and essentially an a M an X intercept happens whenever you have 13 a parentheses or a portion that's equal to zero, 14 right? So for example, this first part B X is equal 15 to zero when X is equal to zero. 16 So that means that we'll have one X intercept at zero right 17 here. And so essentially we're just going to go down the line and look 18 at each individual section of this polynomial and solve for X to see what 19 X would be. And then we'll see how many different Xs we have. 20 So in this case, X minus a, this part here, 21 if I set that equal to zero and I solve for X, 22 then I get the X is equal to positive a so that's another one 23 that I have. I have another X intercepted, 24 a and my next one, 25 it says X minus a is equal to zero. 26 Again, is that if I solve for X, I get the X is equal 27 to X. So this ...