If one zero of the polynomial p(x) = x3 – 6x2 + 11x – 6 is 3, find

1.	If one zero of the polynomial p(x) = x3 – 6x2 + 11x – 6 is 3, find the other two zeroes.
Answer» p(x) = x³ – 6x² + 11x – 6 and its factor, x + 3 Let us divide p(x) by (x – 3). Here, x³ – 6x² + 11x – 6 = (x – 3) (x² – 3x + 2) = (x – 3) [(x² – (2 + 1) x + 2] = (x – 3) (x² – 2x – x + 2) = (x – 3) [x (x – 2) – 1(x – 2)] = (x – 3) (x – 1) (x – 2) ∴The other two zeroes are 1 and 2.

If one zero of the polynomial p(x) = x3 – 6x2 + 11x – 6 is 3, find the other two zeroes.

Answer»

p(x) = x³ – 6x² + 11x – 6 and its factor, x + 3

Let us divide p(x) by (x – 3).

Here, x³ – 6x² + 11x – 6 = (x – 3) (x² – 3x + 2)

= (x – 3) [(x² – (2 + 1) x + 2]

= (x – 3) (x² – 2x – x + 2)

= (x – 3) [x (x – 2) – 1(x – 2)]

= (x – 3) (x – 1) (x – 2)

∴The other two zeroes are 1 and 2.