Question

if alpha and beta are the zeros of x square - 4 x + 3 find a quadratic polynomial whose roots are 3 alpha and 3 Beta​

Answer 1

Hey

$f(x) = x {}^{2} - 4x + 3 \\ \\Given \: that \: \alpha \: an d \: \beta \: are \: the \: zeros\: \\ \\ Sum \: of \: zeros :\\ \alpha + \beta = - ( - 4) = 4 \\ \\ Product \: of \: zeros :\\ \alpha \beta = 3 \\ \\ Now ,\\ \\ let \: S\: and \: P \: denote \: the \: sum \: and \: product \: of \: zeros \: of \: the \: required \: polynomial \\ \\ S= 3 \alpha + 3 \beta = 3( \alpha + \beta ) = 3 \times 4 = 12 \\ \\ P = (3 \alpha )(3 \beta ) = 9 \alpha \beta = 9 \times 3 = 27 \\ \\ Required \: polynomial :\\ x {}^{2} - Sx + P\\ = x {}^{2} - 12x + 27$