Find a cubic polynomial whose zeros are , 1 and –3.

Let the zeros of the polynomial be a, b and c

Where a = 1/2, b = 1 and c = - 3

The cubic polynomial can be calculated as follows:

x^{3} – (a + b + c) x^{2} + (ab + bc + ca) x – abc

Putting the values of a, b and c in the above equation we get:

= x^{3} – (1/2 + 1 - 3) x^{2} + (1/2 – 3 – 3/2)x – (- 3/2)

= x^{3} – (-3/2) x^{2} – 4x + 3/2

= 2x^{3} + 3x^{2} – 8x + 3

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