Explanation for Question 20 From the Math (No Calc) Section on the 2019 March Sat
Question 20 says the function H is defined above where a, 2 B, N C R into your constants. 3 If the zeros of the function are negative five, 4 six, and seven, what is the value of C? 5 So what we have to do is take the zeros and work backwards factor 6 backwards to get the original equation written here at the top. 7 So let's start by writing these out. 8 So if a zero is negative five, that means that one of the factors 9 is X plus five. If a zero is positive six, 10 that means one of the factors is X minus six. 11 And the third one is X minus seven, 12 because this is positive seven. Now we need to distribute. 13 So starting with just these two, we get X square plus negative 14 six plus five X plus negative 30. 15 And that becomes X squared plus negative X plus negative 30. 16 And then finally we have to distribute with X minus seven and we 17 get X plus negative seven X squared plus 18 negative X squared plus negative 30 X plus 19 negative two 10. And when we add and subtract like terms, 20 we get X cubed plus negative eight X squared plus 21 negative 30 X plus negative two, 22 or I'm sorry, positive two 10 positive to 10, 23 because it was negative 30 times negative seven. 24 So that should be positive. And so the answer of 25 what is the value of C this last part is 210.