Correct Answer - Option 3 :
(2q2 – 4pr)/p2
GIVEN:
‘α’ and ‘β’ are the roots of expression px2 + qx + r = 0.
CONCEPT:
Algebra
CALCULATION:
Since ‘α’ and ‘β’ are the roots of expression px2 + qx + r = 0.
α + β = -q/p
αβ = r/p
Now,
(α – β)2 = (α + β)2 – 4αβ
(α – β)2 = (-q/p)2 – 4r/p
2 (α2 + β2) can be written as: 2α2 + 2β2 + 2αβ – 2αβ
= 2α2 + 2β2 + 2αβ – 2αβ
= α2 + β2 + 2αβ + α2 + β2 – 2αβ
= (α + β)2 + (α – β)2
= (-q/p)2 + (-q/p)2 – 4r/p
= q2/p2 + q2/p2 – 4pr/p2
= (2q2 – 4pr)/p2
