Question

If alpha and beta are the zeroes of polynomial 2xsquare - 5x +6 find alpha cube and beta cube

Answer 1

Answer:

${ \alpha }^{3} + { \beta }^{3} = \frac{35}{4} .$

Step-by-step explanation:

$2 {x}^{2} - 5x + 6 =0 \\ \\ \alpha + \beta = \frac{5}{2} \\ \\ \alpha \beta = \frac{6}{2} = 3 \\ \\ { \alpha }^{3} + { \beta }^{3} = ( \alpha + \beta )( { \alpha }^{2} + { \beta }^{2} - \alpha \beta ) \\ \\ = ( \frac{5}{2} )( {( \alpha + \beta )}^{2} -3 \alpha \beta ) \\ \\ = ( \frac{5}{2} )( {( \frac{5}{2} )}^{2} - 3 (3)) \\ \\ = ( \frac{5}{2} )( \frac{25 - 18}{2} ) \\ \\ = \frac{5}{2} ( \frac{7}{2} ) \\ \\ = \frac{35}{4} \: \: \: \: .$