Question

If α and β are the zeroes of the polynomial x^+12x+35 form a quadratic polynomial whose zeroes are 2α and 2β

Answer 1

refer to the attachment

Answer 2

$f(x) = x { }^{2} - 12x + 35 \\ give n \: that \: \alpha \: and \: \beta \: are \: the \: zeros \: of \: given \: polynomial \\ \alpha + \beta = 12 \: \: \: \: \: \: \: \: \alpha \beta = 35 \\ \\ let \: s \: and \: p \: denote \: the \: sum \: and \: the \: product \: of \: zeros \: of \: required \: polynomial \\ \\ s = 2 \alpha + 2 \beta = 2( \alpha + \beta ) = 2 \times 12 = 24 \\ \\ p = 2 \alpha \times 2 \beta = 4 \alpha \beta = 4 \times 35 = 140 \\ \\ \\ required \: polynomial \\ \\ x {}^{2} - sx + p \\ \\ x {}^{2} - 24x + 140$