JEE Main2002MathematicsQuadratic EquationActual

If but ^2=5 -3 and ^2=5 -3 then the equation having / and / as its roots is

Options

A3 x^2-19 x+3=0
B3 x^2+19 x-3=0
C3 x^2-19 x-3=0
Dx^2-5 x+3=0

Correct answer

A. 3 x^2-19 x+3=0

Step-by-step solution

We have ^2=5 -3 aligned & ^2-5 +3=0 = 5 13 2 . Similarly, ^2=5 -3 = 5 13 2 & = 5+ 13 2 and = 5- 13 2 or vice - versa & ^2+ ^2= 50+26 4 =19 & = 1 4 (25-13)=3 aligned Thus, the equation having & as its roots is x^2-x ( + )+ =0 x^2-x ( ^2+ ^2 )+1=0 or 3 x^2-19 x+1=0

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