Explanation for Question 17 From the Math (Calc) Section on the 2019 April Sat
For number 17, we want to know if four X squared plus BX plus 2 nine equals zero, where it be as a constant has exactly one solution. 3 What is the possible value of B? 4 So if you think about when we factor polynomials, 5 if we ended up factoring and it's, 6 let's say X plus four squared, 7 as an example, to find the zeros, 8 we would set it equal to zero. So X plus four X 9 plus four, there are our two factors. 10 We would set them both equal to zero and 11 we would get X equals negative four for both of them. 12 So for this example, our solution is at X equals negative four. 13 It is only one solution because technically we got two solutions. 14 It's just the same solution twice, 15 which leaves us with one solution. So we're going to take this idea and 16 apply it to this polynomial. 17 So what we're looking for is a way to factor it. 18 That would give us two solutions that are identical, 19 which would technically just be one solution. 20 So here we have four X squared plus BX plus nine. 21 If you think about when you foil this first number has to 22 be the first numbers of each factor multiplied together. 23 So if we think about the square root of four X squared, 24 that is going to be two X, 25 because two X times two X gives you four 26 X squared. So, uh, have the two X at the beginning of both 27 factors. So now, 28 if we think about our last number, 29 that's going to be this last number of times, 30 this last number. So the square root of nine is three. 31 I'm goi...