Quadratic EquationMedium
Question
Let α, β be the roots of the equation x2 - px + r = 0 and 
, 2β be the roots of the equation x2 - qx + r = 0. Then the value of r is
, 2β be the roots of the equation x2 - qx + r = 0. Then the value of r isOptions
A.
(p - q)(2q - p)
(p - q)(2q - p)B.(q - p)(2p - q)
(q - p)(2p - q)C.(q - 2p)(2q - p)
(q - 2p)(2q - p)D.(2p - q)(2q - p)
(2p - q)(2q - p)Solution
The equation x2 - px + r = 0 has roots (α, β) and the equation
x2 - qx + r = 0 has roots
.
⇒ r = αβ and α + β = p and
+ 2β = q
⇒ β =
and α = 
⇒ αβ = r =
(2q - p)(2p - q).
x2 - qx + r = 0 has roots
. ⇒ r = αβ and α + β = p and
+ 2β = q⇒ β =
and α = ⇒ αβ = r =
(2q - p)(2p - q).Create a free account to view solution
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