Question

if a &ß are zeroes of x^2+x-1 then find a^2×ß+a×ß^2​

Answer 1

$Given \: \: Question \: \: Is \: \: \\ \\f(x) = x {}^{2} + x - 1 \\ \alpha \: \: \: and \: \: \beta \: \: \: are \: its \: two \: zeroes \: \\ \\ Answer \: \\ \\ \alpha + \beta = \frac{ - 1}{1} \: \: \: and \: \: \: \: \alpha \beta = \frac{ - 1}{ 1} \\ \\ \alpha {}^{2} \beta + \beta {}^{2} \alpha = \alpha \beta ( \alpha + \beta ) \\ \\ \alpha { }^{2} \beta + \beta {}^{2} \alpha = - 1( - 1) \\ \\ \alpha { }^{2} \beta + \beta {}^{2} \alpha = 1 \\ \\ Therefore \: \: \: \alpha {}^{2} \beta + \beta {}^{2} \alpha = 1 \\ \\ Note \: \: \: \\ \\ for \: a \: general \: quadratic \: polynomial \: \\ say \: \: \: p(x) = ax {}^{2} + bx + c \\ \\ \alpha + \beta = \frac{ - b}{ a} \: \: \: \: \: \: and \: \: \: \: \: \alpha \beta = \frac{c}{a}$