If $\alpha ,\;\beta $ are the roots of ${x^2} - ax + b = 0\;\,{\rm{and\;if}}\,\;{\alpha ^n} + {\beta ^n} = {V_n},$ then

${V_{n + 1}} = a{V_n} + a{V_{n - 1}}$

${V_{n + 1}} = a{V_{n - 1}} - b{V_n}$

JEE MATHEMATICS MCQ: QUADRATIC EQUATIONS

1 Hard

1 of 1

Application +4 | -1

\alpha ,\;\beta

are the roots of

{x^2} - ax + b = 0\;\,\mathrm{and\;if}\,\;{\alpha ^n} + {\beta ^n} = {V_n},

then

View answer and explanation

Correct option: C

{V_{n + 1}} = a{V_n} - b{V_{n - 1}}

Option C (

{V_{n + 1}} = a{V_n} - b{V_{n - 1}}

) is correct because it is derived by using the given recurrence relation and properties of roots of the quadratic equation.

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