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Find a cubic polynomial with the sum of its zeroes, sum of the

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Find a cubic polynomial with the sum of its zeroes, sum of the products of its zeroes taken two at a time and product of its zeroes as the numbers given below: $\frac{2}{5}, \frac{1}{10}, \frac{1}{2}$

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Find a cubic polynomial with the sum of its zeroes, sum of the products of its zeroes taken two at a time and product of its zeroes as the numbers given below:

\frac{2}{5}, \frac{1}{10}, \frac{1}{2}

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Text solutionVerified

Let the zeroes be

α, β

and

γ

.
Then, we have

α + β + γ = \frac{2}{5}

α β + β γ + γ α = \frac{1}{10}

α β γ = \frac{1}{2}

Now , required cubic polynomial

= x^{3} - (α + β + γ) x^{2} + (α β + β γ + γ α) x - α β γ

= x^{3} - (\frac{2}{5}) x^{2} + (\frac{1}{10}) x - (\frac{1}{2})

= \frac{10 x ^{3} - 4 x ^{2} + x - 5}{10}

So,

10 x^{3} - 4 x^{2} + x - 5

is the required cubic polynomial which satisfy the given conditions.

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Question Text	Find a cubic polynomial with the sum of its zeroes, sum of the products of its zeroes taken two at a time and product of its zeroes as the numbers given below: $\frac{2}{5}, \frac{1}{10}, \frac{1}{2}$
Answer Type	Text solution:1
Upvotes	150

Find a cubic polynomial with the sum of its zeroes, sum of the products of its zeroes taken two at a time and product of its zeroes as the numbers given below: 52​,101​,21​

Text solutionVerified

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Find a cubic polynomial with the sum of its zeroes, sum of the products of its zeroes taken two at a time and product of its zeroes as the numbers given below: $\frac{2}{5}, \frac{1}{10}, \frac{1}{2}$