Which of the following values of is a zero of
A zero of a function is an input that makes its output . When the choices give possible inputs, define the function in Desmos and evaluate a candidate with simple powers; you can stop when the output is . Don't reject an input because it's negative. The whole output, not the sign of the input, settles the question.
Hints
- Hint 1
Function notation means put in for every in the rule. A zero needs the resulting output to equal . What would you check for one candidate?
- Hint 2
Choose a candidate with simple powers. Enter the function once in Desmos, then evaluate that input. Check the complete output, including the coefficients and the constant term.
Step-by-step
Test a candidate in Desmos
Step 1Identify what a zero must do
Call a proposed input . A zero is an input that makes the whole output equal : . So you only need to find one choice that passes this test, not every zero of the function.
- Step 2
Evaluate the quickest candidate
Try first because its powers stay , making it a quick candidate. Type on one Desmos line and on the next. Desmos prints , so is a zero of the given function. Choice D.