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3 years ago

Write a polynomial function of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros.

Mathematics

1 answer:

kogti [31]3 years ago

6 0

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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