Question

If α and β are the zeroes of the polynomial 2x^2 - 3x + 1 form a quadratic polynomial whose zeroes are 3α and 3β ​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

$if \: f(x) \: is \: a \: polynomial \: with \: roots \: \alpha \: and \: \beta \\ \\ then \: the \: polynomial \: with \: roots \: k \alpha \: and \: k \beta \: is \: f( \frac{x}{k} ) = 0$

$given \\ \\ f(x) = 2 {x}^{2} - 3x + 1 \\ \\ now \\ \\ f( \frac{x}{3} ) = 0 \\ \\ 2 \frac{ {x}^{2} }{9} - 3 \times \frac{x}{3} + 1 = 0 \\ \\ 2 {x}^{2} - 9x + 9 = 0$

$PROOF \\ \\ f(x) = {x}^{2} - ( \alpha + \beta )x + \alpha \beta = 0 \\ \\ now \\ \\ {x}^{2} - k( \alpha + \beta )x + {k}^{2} \alpha \beta = 0 \\ \\ \frac{ {x}^{2} }{ {k}^{2} } - ( \alpha + \beta ) \times \frac{x}{k} + \alpha \beta = 0 \\ \\ f( \frac{x}{k} ) = 0$

hope it helps