Question

quadratic polynomial 2x²-3x+1 has zeros as Alfa &bita . from a quadratic polynomial whose zeroes are 3alfa &3bita​

Answer 1

Step-by-step explanation:

$2x { }^{2} - 3x + 1 \\ 2x {}^{2} - 2x - x + 1 \\ 2x(x - 1) - 1(x - 1) \\ (2x - 1)(x - 1) \\ \alpha = 2x - 1 = 0 \\ \alpha = \binom{1}{2 } \: \: \: \: \: \beta = 1 \\ 3 \alpha + 3 \beta = \binom{3}{2} \\ 3 \alpha \times 3 \beta = 9 \times \binom{1}{2} \times 1 = \binom{9}{2} \\ p(x) = x {}^{2} - sx + p = 0 \\ x { }^{2} - \binom{3}{2}x + \binom{9}{2} = 0 \\ \binom{2x {}^{2} - 3 x + 9}{2} = 0 \\ 2x^{2} - 3x + 9 = 0 \\ \\ \\ i.e \: 2x {}^{2} - 3x + 9 \: is \: required \: polynomial \: with \: 3 \alpha \: and \: 3 \beta \: as \: its \: zeroes$