Question

If α and β are the zeroes of a polynomial such that α + β = -7 and αβ = 10, then find the polynomial.

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Answer 1

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x² + 7x + 10 is the required polynomial.

Explanation :

According to the Question

It is given that α and β are the zeroes of a polynomial .

Sum of zeros (α+β) = -7

Product of Zeros (αβ) = 10

we need to calculate the polynomial.

As we know that if the sum of zeros and product of zeros are given we can easily calculate the polynomial .

Let the Polynomial be P(x)

• P(x) = x²-(sum of zeros)x + (product of zeros)

Substitute the value we get

➻ P(x) = x²-(-7)x + (10)

➻ P(x) = x²+7x+10

So, the required polynomial is x² + 7x + 10.

Step-by-step explanation:

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Answer 2

Step-by-step

x² + 7x + 10 is the required polynomial.

x² + 7x + 10 is the required polynomial.Explanation :

x² + 7x + 10 is the required polynomial.Explanation :According to the Question

x² + 7x + 10 is the required polynomial.Explanation :According to the QuestionIt is given that α and β are the zeroes of a polynomial .

x² + 7x + 10 is the required polynomial.Explanation :According to the QuestionIt is given that α and β are the zeroes of a polynomial .Sum of zeros (α+β) = -7

x² + 7x + 10 is the required polynomial.Explanation :According to the QuestionIt is given that α and β are the zeroes of a polynomial .Sum of zeros (α+β) = -7Product of Zeros (αβ) = 10

x² + 7x + 10 is the required polynomial.Explanation :According to the QuestionIt is given that α and β are the zeroes of a polynomial .Sum of zeros (α+β) = -7Product of Zeros (αβ) = 10we need to calculate the polynomial.

x² + 7x + 10 is the required polynomial.Explanation :According to the QuestionIt is given that α and β are the zeroes of a polynomial .Sum of zeros (α+β) = -7Product of Zeros (αβ) = 10we need to calculate the polynomial.As we know that if the sum of zeros and product of zeros are given we can easily calculate the polynomial .

x² + 7x + 10 is the required polynomial.Explanation :According to the QuestionIt is given that α and β are the zeroes of a polynomial .Sum of zeros (α+β) = -7Product of Zeros (αβ) = 10we need to calculate the polynomial.As we know that if the sum of zeros and product of zeros are given we can easily calculate the polynomial .Let the Polynomial be P(x)

x² + 7x + 10 is the required polynomial.Explanation :According to the QuestionIt is given that α and β are the zeroes of a polynomial .Sum of zeros (α+β) = -7Product of Zeros (αβ) = 10we need to calculate the polynomial.As we know that if the sum of zeros and product of zeros are given we can easily calculate the polynomial .Let the Polynomial be P(x)• P(x) = x²-(sum of zeros)x + (product of zeros)

x² + 7x + 10 is the required polynomial.Explanation :According to the QuestionIt is given that α and β are the zeroes of a polynomial .Sum of zeros (α+β) = -7Product of Zeros (αβ) = 10we need to calculate the polynomial.As we know that if the sum of zeros and product of zeros are given we can easily calculate the polynomial .Let the Polynomial be P(x)• P(x) = x²-(sum of zeros)x + (product of zeros)Substitute the value we get

x² + 7x + 10 is the required polynomial.Explanation :According to the QuestionIt is given that α and β are the zeroes of a polynomial .Sum of zeros (α+β) = -7Product of Zeros (αβ) = 10we need to calculate the polynomial.As we know that if the sum of zeros and product of zeros are given we can easily calculate the polynomial .Let the Polynomial be P(x)• P(x) = x²-(sum of zeros)x + (product of zeros)Substitute the value we get➻ P(x) = x²-(-7)x + (10)

x² + 7x + 10 is the required polynomial.Explanation :According to the QuestionIt is given that α and β are the zeroes of a polynomial .Sum of zeros (α+β) = -7Product of Zeros (αβ) = 10we need to calculate the polynomial.As we know that if the sum of zeros and product of zeros are given we can easily calculate the polynomial .Let the Polynomial be P(x)• P(x) = x²-(sum of zeros)x + (product of zeros)Substitute the value we get➻ P(x) = x²-(-7)x + (10)➻ P(x) = x²+7x+10

x² + 7x + 10 is the required polynomial.Explanation :According to the QuestionIt is given that α and β are the zeroes of a polynomial .Sum of zeros (α+β) = -7Product of Zeros (αβ) = 10we need to calculate the polynomial.As we know that if the sum of zeros and product of zeros are given we can easily calculate the polynomial .Let the Polynomial be P(x)• P(x) = x²-(sum of zeros)x + (product of zeros)Substitute the value we get➻ P(x) = x²-(-7)x + (10)➻ P(x) = x²+7x+10So, the required polynomial is x² + 7x + 10.

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