Which of the following are possible rational roots of the polynomial function?Check all that apply.F(x) = 5x2 - 3x + 3A.± 5± 5B.± 3± 3C.± 1± 1D.±15± 51 E.± 13± 31 SUBMITarrow_backPREVIOUS
Question
Which of the following are possible rational roots of the polynomial function?Check all that apply.F(x) = 5x2 - 3x + 3A.± 5± 5B.± 3± 3C.± 1± 1D.±15± 51 E.± 13± 31 SUBMITarrow_backPREVIOUS
Solution
The rational root theorem states that the possible rational roots of a polynomial equation are ± factors of the constant term / ± factors of the leading coefficient.
In this case, the constant term is 3 and the leading coefficient is 5.
The factors of 3 are 1 and 3, and the factors of 5 are 1 and 5.
So, the possible rational roots are ±1/1, ±1/5, ±3/1, ±3/5.
Simplifying these gives us ±1, ±1/5, ±3, ±3/5.
So, the possible rational roots that apply from the given options are:
A. ±5 (does not apply) B. ±3 (applies) C. ±1 (applies) D. ±15 (does not apply) E. ±1/3 (does not apply)
So, the possible rational roots from the given options are B. ±3 and C. ±1.
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