Question

Find a cubic polynomial whose zeroes are `1/2`, 1 and –3.

Answer 1

If the zeroes of the cubic polynomial are a, b and c then the cubic polynomial can be found as  

x³ – (a + b + c)x² + (ab + bc + ca)x – abc   ...(1) 

Let a = `1/2`, b = 1 and c = –3 

Substituting the values in (1), 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` 

⇒ 2x³ + 3x² – 8x + 3