Write a polynomial function of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros.
1 answer:
9514 1404 393
Answer:
f(x) = x³ -5x² +2x +8
Step-by-step explanation:
If the function has a zero of p, then it has a factor of (x-p). The polynomial of least degree will only have factors corresponding to the given zeros:
f(x) = (x -(-1))(x -2)(x -4)
= (x +1)(x -2)(x -4)
= (x² -x -2)(x -4)
f(x) = x³ -5x² +2x +8
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