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α²+β²=53

⇒(α+β)²-2αβ=53

⇒(5)²-2αβ=53

⇒-2αβ=53-25

⇒-2αβ=28

⇒αβ=-14

The required polynomial whose roots are α and β is

x²+(α+β)x-αβ

⇒x²+5x-14

Hope this helped you!!!!!!

⇒(α+β)²-2αβ=53

⇒(5)²-2αβ=53

⇒-2αβ=53-25

⇒-2αβ=28

⇒αβ=-14

⇒(5)²-2αβ=53

⇒-2αβ=53-25

⇒-2αβ=28

⇒αβ=-14