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  3. the cubic polynomial equation x + bx + cx + d = 0

The cubic polynomial equation x + bx + cx + d = 0 has three...

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The cubic polynomial equation x + bx + cx + d = 0 has three roots X?, X2, and X3.By expanding the product (x-x?)(x - x?)(x - x3), show thata) i) b = (x? + x? + x3);ii) c = x?x? + x? x3 + x2X3;iii) d = -X?X2X3.It is given that b = -9 and c = 45 for parts b) and c) below.b) i) In the case that the three roots x?, x2, and x3 form an arithmetic sequence, show that oneof the roots is 3.ii) Hence, determine the value of d.c) In another case the three roots form a geometric sequence. Determine the value of d.

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