Find the cubic polynomial whose sum of zeros is 3, sum of the product of its zeros taken two at a time is −1 and product of its zeros is −3

Video Explanation

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Solution

Given:

Sum of zeros = 3
Sum of products of zeros taken two at a time = −1
Product of zeros = −3

Let the zeros of the required cubic polynomial be α, β and γ.

Step 1: Use the Standard Form of a Cubic Polynomial

A cubic polynomial with zeros α, β and γ is:

x³ − (α + β + γ)x² + (αβ + βγ + γα)x − αβγ

Step 2: Substitute the Given Values

x³ − (3)x² + (−1)x − (−3)

= x³ − 3x² − x + 3

Final Answer

The required cubic polynomial is x³ − 3x² − x + 3.

Conclusion

Thus, the cubic polynomial whose sum of zeros is 3, sum of the product of its zeros taken two at a time is −1 and product of its zeros is −3 is x³ − 3x² − x + 3.