6. If α and β are
the roots of the equation x2 – 5x + 6 = 0, find
(i) α2+β2
(ii) α/β +β/α
Sol. x2
– 5x + 6 = 0
Comparing with
ax2 + bx + c = 0 we have a = 1, b = -5, c = 6
α and β are the
roots of the given quadratic equation, [Given]
α + β
= -b/a = -(-5)/1 = 5
Also, αβ = c/a = 6/1 = 6
(i) α2+β2 = (α + β )2 – 2αβ = 52 – 2 (6) =
25 – 12 = 13
(ii) α/β +β/α
= (α2 + β2)/ αβ = 13/6
