If α and β are roots of x²−5x+2=0, find α²β+αβ²+α²+β².

Question

G1 Physics · Accepted Answer

Here α+β=5 and αβ=2. First α²β+αβ²=αβ(α+β)=2×5=10. Also α²+β²=(α+β)²−2αβ=25−4=21. Total=10+21=31.