Question

If the zeroes of the polynomial x³ – 3x² + x + 1 are (a – b), a and (a + b), find the values of a and b.

Answer 1

The given polynomial = x³ – 3x² + x + 1 and its roots are (a – b), a and (a + b). 

Comparing the given polynomial with Ax³ + Bx² + Cx + D, 

we have: 

A = 1, B = -3, C = 1 and D = 1 

Now, (a – b) + a + (a + b) = \(\frac{-B}A\)

⇒ 3 a = – \(\frac{-3}1\)

⇒ a = 1 

Also, (a – b) × a × (a + b) = \(\frac{-D}A\)

⇒ a (a² – b² ) = \(\frac{-1}1\)

⇒ 1 (1² – b² ) = -1 

⇒ 1– b² = -1 

⇒ b² = 2 

⇒ b = ±√2 

∴ a = 1 and b = ±√2