Question

write a cubic polynomial whose roots are 1 , -1,-2

Answer 1

Answer:

Cubic polynomial = (x - 1)(x + 1)(x + 2)

= (x² - 1)(x + 2)

= x³ + 2x² - x - 2

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Answer 2

The cubic polynomial whose roots are 1 , - 1 , - 2 is x³ + 2x² - x - 2

Given :

The roots of a cubic polynomial 1 , - 1 , - 2

To find :

The cubic polynomial

Solution :

Step 1 of 2 :

Write down the roots

Here it is given that the roots of the cubic polynomial are 1 , - 1 , - 2

Step 2 of 2 :

Find the polynomial

We know that if a , b , c are roots are of a cubic polynomial then the cubic polynomial is

(x - a) (x - b) (x - c) = 0

Hence the required cubic polynomial

= (x - 1)(x + 1)(x + 2)

= (x² - 1²)(x + 2) [ ∵ a² - b² = (a + b) (a - b) ]

= (x² - 1)(x + 2)

= x²(x + 2) - 1(x + 2)

= x³ + 2x² - x - 2

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