Quadratic EquationHard
Question
If α ≠ β but α2 = 5α - 3 and β3 = 5β - 3 then the equation having α/β and β/α as its roots is
Options
A.3x2 - 19 x + 3 = 0
B.3x2 + 19 x - 3 = 0
C.3x2 - 19 x - 3 = 0
D.x2 - 5x + 3 = 0
Solution
We have α2 = 5α - 3
⇒ α2 - 5α + 3 = 0 ⇒ α =
. Similarly, β2 = 5β - 3 ⇒ α =
∴ α =
and β = 
or vice - versa
α2 + β2 =
= 19 & αβ = 
(25 - 13)= 3
Thus, the equation having
as its roots is
x2 - x
+ 
= 0 ⇒ x2 - x 
+ 1 = 0 or 3x2 - 19x + 1 = 0
⇒ α2 - 5α + 3 = 0 ⇒ α =
. Similarly, β2 = 5β - 3 ⇒ α = ∴ α =
and β = or vice - versaα2 + β2 =
= 19 & αβ = (25 - 13)= 3 Thus, the equation having
as its roots is x2 - x
+ = 0 ⇒ x2 - x + 1 = 0 or 3x2 - 19x + 1 = 0Create a free account to view solution
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