If α and β are the roots of the equation x2 – 5x + 6 = 0, find (i) α2+β2 (ii) α/β +β/α

6. If  α  and β  are the roots of the equation x2 – 5x + 6 = 0, find


(i) α22



(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) α22 = (α + β )2 – 2αβ = 52 – 2 (6) = 25 – 12 = 13


(ii) α/β +β/α = 2 + β2)/ αβ = 13/6