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Question: Find a polynomial function in standard form with real coefficients whose zeros are 3 and - 5 and multiplicity is 2 and 2.
A ) f(x) = x4-26x2+225
B ) f(x) = x4+4x3-26x2-60x+225
C ) f(x) = x4+4x3-60x
D ) f(x) = x4+26x2+225
Steps to derive
1 The factor corresponding to the zero 3 with multiplicity 2 is (x - 3)2.
2 The factor corresponding to the zero - 5 with multiplicity 2 is (x + 5)2.
3 Hence, the polynomial function with the given zeros is f(x) = (x - 3)2(x + 5)2
4 = (x2 - 6x + 9)(x2 + 10x + 25)
5 So, the standard form of the polynomial function with given zeros is f (x) = x4+4x3-26x2- 60x + 225.
Hence the right answer is Option B
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