SAT Quadratic Functions

Correct Answer: C

Solution 1:

Notice that if $x<1$ , then $x-2<0$ and $1-x>0$ . That is, neither factor can equal $0$ . Hence, the only way for $k(x-2)(1-x)$ to equal $0$ is if $k=0$ .

Solution 2:

$k(x-2)(1-x)=0$ if $k=0, x=2,\ \text{or}\ x=1$ . But, $x<1$ . Therefore $x\neq 1, x\neq 2$ and $k$ must equal $0.$

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Incorrect Choices:

(A) , (B) , (D) , and (E)
These wrong choices are intended to make you think of the values of $x$ that would make the equation equal $0.$ But the question is about $k$ , not about $x$ .