jee-main 2020 Q51

jee-main · India · session1_07jan_shift2 Roots of polynomials Vieta's formulas: compute symmetric functions of roots

Let $\alpha$ and $\beta$ be the roots of the equation $x ^ { 2 } - x - 1 = 0$. If $p _ { k } = ( \alpha ) ^ { k } + ( \beta ) ^ { k } , k \geq 1$, then which one of the following statements is not true?
(1) $p _ { 3 } = p _ { 5 } - p _ { 4 }$
(2) $p _ { 5 } = 11$
(3) $\left( p _ { 1 } + p _ { 2 } + p _ { 3 } + p _ { 4 } + p _ { 5 } \right) = 26$
(4) $p _ { 5 } = p _ { 2 } \cdot p _ { 3 }$

Let $\alpha$ and $\beta$ be the roots of the equation $x ^ { 2 } - x - 1 = 0$. If $p _ { k } = ( \alpha ) ^ { k } + ( \beta ) ^ { k } , k \geq 1$, then which one of the following statements is not true?\\
(1) $p _ { 3 } = p _ { 5 } - p _ { 4 }$\\
(2) $p _ { 5 } = 11$\\
(3) $\left( p _ { 1 } + p _ { 2 } + p _ { 3 } + p _ { 4 } + p _ { 5 } \right) = 26$\\
(4) $p _ { 5 } = p _ { 2 } \cdot p _ { 3 }$

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