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

1.	Find a cubic polynomial whose zeroes are 1/2 , 1 and –3.
Answer» 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 x³ – ( 1/2 + 1 − 3)x² + ( 1/2 − 3 − 3/2 )x – ( −3/2 ) ⇒ x³ – ( −3/2 )x² – 4x + 3/2 ⇒ 2x³ +3x² – 8x + 3

Answer»

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

x³ – ( 1/2 + 1 − 3)x² + ( 1/2 − 3 − 3/2 )x – ( −3/2 )

⇒ x³ – ( −3/2 )x² – 4x + 3/2

⇒ 2x³ +3x² – 8x + 3

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