Quadratic EquationEasy
Question
Difference between the corresponding roots of x2 + ax + b = 0 and x2 + bx + a = 0 is same and a × b, then
Options
A.a + b + 4 = 0
B.a + b - 4 = 0
C.a - b - 4 = 0
D.a - b + 4 = 0
Solution
Let α, β and y, δ are the roots of the equations
x2 + ax + b = 0 and x2 + bx + a = 0 ∴ α + β = - a, αβ = b and y + δ = - b, yδ = a
Given α - β = y - δ ⇒ (α - β)2 = (y - δ)2 ⇒ (α + β)2 - 4αβ = (y + δ)2 - 4yδ
⇒ a2 - 4b = b2 - 4a ⇒ (a2 - b2) + 4 (a - b) = 0 ⇒ a + b + 4 = 0 (∵ a ≠ b)
x2 + ax + b = 0 and x2 + bx + a = 0 ∴ α + β = - a, αβ = b and y + δ = - b, yδ = a
Given α - β = y - δ ⇒ (α - β)2 = (y - δ)2 ⇒ (α + β)2 - 4αβ = (y + δ)2 - 4yδ
⇒ a2 - 4b = b2 - 4a ⇒ (a2 - b2) + 4 (a - b) = 0 ⇒ a + b + 4 = 0 (∵ a ≠ b)
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