Question

Example 28. Find cubic polynomial with the sum, sum of the product of its zeroes taken two at a time, and the product of its zeroes as 5, -7, -14 respectively.

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Answer 1

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Given:-

• sum of the product of its zeroes taken two at a time
• the product of its zeroes as 5, -7, -14 respectively

Find:-

• Find cubic polynomial with the sum of the product of its zeroes.

Answer:-

Let the zeroes be α, β and γ.

Then, we have

α + β + γ = 5

αβ + βγ + γα = -7

αβγ = -14

Now, required cubic polynomial

=> x³ - (α + β + γ)x² + (αβ + βγ + γα)x - αβγ

=> x³ - 5x² + (-7)x - (-14)

=> x³ - 5x - 7x + 14

So, x³ - 5x - 7x + 14 is the required cubic polynomial which satisfy the given conditions.

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