Let alpha and beta be the roots of the equati | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Since $\alpha$ and $\beta$ are roots of $5x^{2} + 6x - 2 = 0$,they satisfy the equation.$5\alpha^{2} + 6\alpha - 2 = 0 \implies 5\alpha^{n+2} + 6\

Vedclass · Accepted Answer

$5S_{6} + 6S_{5} = 2S_{4}$

Vedclass · Answer

(A) Since $\alpha$ and $\beta$ are roots of $5x^{2} + 6x - 2 = 0$,they satisfy the equation.$5\alpha^{2} + 6\alpha - 2 = 0 \implies 5\alpha^{n+2} + 6\alpha^{n+1} - 2\alpha^{n} = 0$ (multiplying by $\alpha^{n}$).Similarly,$5\beta^{n+2} + 6\beta^{n+1} - 2\beta^{n} = 0$.Adding these two equations,we get $5(\alpha^{n+2} + \beta^{n+2}) + 6(\alpha^{n+1} + \beta^{n+1}) - 2(\alpha^{n} + \beta^{n}) = 0$.This simplifies to $5S_{n+2} + 6S_{n+1} - 2S_{n} = 0$.For $n = 4$,we have $5S_{6} + 6S_{5} - 2S_{4} = 0$,which implies $5S_{6} + 6S_{5} = 2S_{4}$.

Let $\alpha$ and $\beta$ be the roots of the equation $5x^{2} + 6x - 2 = 0$. If $S_{n} = \alpha^{n} + \beta^{n}$ for $n = 1, 2, 3, \dots$,then:

Similar Questions

If the sum of two roots of the equation $x^3-2px^2+3qx-4r=0$ is zero,then the value of $r$ is

If $\lambda$ is the ratio of the roots of the quadratic equation in $x$,$3m^2x^2 + m(m - 4)x + 2 = 0$,then the least value of $m$ for which $\lambda + \frac{1}{\lambda} = 1$ is:

Let $\alpha$ and $\beta$ be the roots of the equation $p x^2 + q x + r = 0$,where $p \neq 0$. If $p, q, r$ are in $AP$ and $\frac{1}{\alpha} + \frac{1}{\beta} = 4$,then the value of $|\alpha - \beta|$ is

If $\alpha$ and $\beta$ are the roots of $x^2-2x+4=0$,then the value of $\alpha^6+\beta^6$ is

If $\alpha$ and $\beta$ are the roots of the equation $ax^2 + bx + c = 0$,then what are the roots of the equation $cx^2 + bx + a = 0$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module