Question

α+β=5 and α²+β²=53, find a Quadratic Equation whose roots are α and β.

Answer 1

α+β=5
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!!!!!!

Answer 2

⇒(α+β)²-2αβ=53
⇒(5)²-2αβ=53
⇒-2αβ=53-25
⇒-2αβ=28
⇒αβ=-14