Question

alpha and beta are the polynomial of the p(x)ax2+bx+c then find alpha cube+ beta cube​

Answer 1

Answer:

$\huge \bf{question } \\ \\ if \: \alpha \: and \: \beta \: are \: the \: polynomials \: of \\ a {x}^{2} + bx + c = 0 \: find \: \: { \alpha}^{3} \: + { \beta}^{3} \\ \\ \huge \red{\bf{solution}} \\ \\ \\ \implies \alpha + \beta = \frac{ - b}{a} \\ \implies \: \alpha \beta = \frac{c}{a} \\ \\ now \: \\ \\ \implies { \alpha}^{3} + { \beta}^{3} = ( \alpha + \beta)( { \alpha}^{2} + { \beta}^{2} - \alpha \beta) \\ \\ \implies { \alpha}^{3} + { \beta}^{3} = ( \frac{ - b}{a} ) \bigg( {( \alpha + \beta)}^{2} - 3 \alpha \beta \bigg) \\ \\ \implies \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{ - b}{a} \bigg( \frac{ {b}^{2} }{ {a}^{2} } - 3 \frac{c}{a} \bigg)$