Question

If Alpha and Beta are zeroes of the polynomial......

Chptr Polynomials- Class 10​

Answer 1

$25 {x}^{2} - 15x + 2 = 0 \\ \\ 25 {x}^{2} - 10x - 5x + 2 = 0 \\ \\ 5x(5x - 2) - 1(5x - 2) = 0 \\ \\ (5x - 1)(5x - 2) = 0 \\ \\ x = \frac{2}{5} \\ \\ x = \frac{1}{5} \\ \\ \alpha = \frac{2}{5} \\ \\ \beta = \frac{1}{5} \\ \\ now \: \: polynomial \: with \: roots \: \frac{1}{ \alpha } \: \: and \: \: \frac{1}{ \beta } \: is \\ \\ {x}^{2} - ( \frac{1}{ \alpha } + \frac{1}{ \beta } ) + \frac{1}{ \alpha \beta } = 0 \\ \\ ( \alpha \beta ) {x}^{2} - ( \alpha + \beta ) + 1 = 0 \\ \\ \frac{2}{25} {x}^{2} - \frac{3}{5} + 1 = 0 \\ \\ 2 {x}^{2} - 15x + 25 = 0$

Or

$f(x) = 25 {x}^{2} - 15x + 2 \\ \\ now \: polynomial \: with \: inverse \: roots \: is \\ \\ f( \frac{1}{x} ) = 0 \\ \\ 25( \frac{1}{ {x}^{2} } ) - 15( \frac{1}{x} ) + 2 = 0 \\ \\ \frac{ 2 {x}^{2} - 15x + 25}{ {x}^{2} } = 0 \\ \\ 2 {x}^{2} - 15x + 25 = 0$

hope it helps

Answer 2

Answer:

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