Question

If α and β are the zeroes of a polynomial such that α + β = -6 and αβ = 5, then find the polynomial.​

Answer 1

Step-by-step explanation:

ANSWER

If α and β are the zeroes of the quadratic polynomial, then

aα2+bα+c=0  and

aβ2+bβ+c=0

or, aα2+bα-aβ2−bβ=0

Then, α+β=a−b

and αβ=abc.

Answer 2

Answer:

♣ ANSWER :

• Quadratic Polynomial = x² + 6x + 5

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Step-by-step explanation:

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♣ QUESTION :

If α and β are the zeroes of a polynomial such that α + β = -6 and αβ = 5, then find the polynomial.

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♣ ANSWER :

• Quadratic Polynomial = x² + 6x + 5

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♣ GIVEN :

• α + β = -6

• αβ = 5

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♣ KNOWLEDGE REQUIRED :

• Quadratic Polynomial = x² - (Sum of zeros)x + Product of zeros

• Quadratic Polynomial = x² - (α + β)x + αβ

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♣ SOLUTION :

• Quadratic Polynomial = x² - (α + β)x + αβ

• Quadratic Polynomial = x² - (-6)x + 5

• Quadratic Polynomial = x² + 6x + 5

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♣ SOME RELATED FORMULAS :-

☞ For quadratic polynomial :

α + β = -b/a

αβ = c/a

☞ For cubic polynomial :

α + β + γ = -b/a

αβγ = -d/a

αβ + βγ + γα = c/a

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♥ Happy Learning ☺️