Question

Write the quadratic polynomial whose zeroes are 2,-4​

Answer 1

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Answer 2

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• Zeroes of Quadratic polynomial are 2 and - 4

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• What's the quadratic polynomial?

Formula to be used :-

• x² - (α + β)x + αβ

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We know,

Formula for quadratic polynomial is ___

x² -(α + β)x + αβ

Where,

(α + β) = sum of zeroes

αβ = product of zeroes

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Let α and β are zeroes of required polynomial.

Let α = 2

and β = -4

Therefore,

Product of zeroes = αβ

⟶ αβ = 2 × (-4)

⟶ αβ = -8 ⠀⠀

_____________

Sum of zeroes = α + β

⟶ α + β = 2 + (-4)

⟶ α + β = 2 - 4

⟶ α + β = -2 ⠀

⠀

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Now, put the values of α + β and αβ in the formula.

⟶ x² - (α + β)x + αβ

⟶ x² -(-2)x + (-8)

⟶ x² + 2x - 8

Hence , the quadratic polynomial is x² + 2x - 8.