Question 3:

If the zeroes of polynomial x³ − 3x² + x + 1 are a − b, a, a + b, find a and b.

Answer:

p(x) = x³ − 3x² + x + 1

Zeroes are a − b, a + a + b

Comparing the given polynomial with px³ + qx² + rx + t, we obtain p = 1, q = −3, r = 1, t = 1 

Sum of zeroes = a − b + a + a + b

The zeroes are 1 − b, 1, 1 + b

Multiplication of zeroes = 1(1 − b) (1 + b)

Hence, a = 1 and b = √2 or – √2

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