Multiple Choice Questions

If alpha and szlig are the roots of the equation 3x2 2x 1 0 then the equation wh...........

Mathematics (NDA) Algebra

If α and ß are the roots of the equation 3x² +2x + 1 = 0, then the equation whose roots are α +ß^-1 and ß + α^-1 is -

3x² + 8x +16 = 0

. 3x² − 8x − 16 = 0

. 3x²+ 8x −16 = 0

x² + 8x + 16 = 0

Sum of roots (α+β) = −2 / 3

Product of roots (αβ) = 1 / 3

Now, P = α + β + 1/ α + 1 / β = −2 / 3 – 2 = -8/3

Q = (α + β^-1 ) (β + α^-1 ) = 16/3

So required equation will be of form x² – P x + Q = 0

Or, 3 x² + 8 x + 16 = 0

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