Question

if alpha and beta are the zeros of the polynomial P (X )
$= 3 {x}^{2} - 12x + 15$
find the value of Alpha square plus beta square​

Answer 1

Step-by-step explanation:

$\huge\underline{\underline{\sf ANSWER}} \\ \alpha \: and \: \beta \: are \: roots \: of \: \\ 3 {x}^{2} - 12x + 15 \\ \\ \alpha + \beta = - \frac{b}{a} = - (\frac{ - 12}{3} ) = \frac{12}{3} = 4 \\ \alpha \beta = \frac{c}{a} = \frac{15}{3} = 5 \\ \\ for \: { \alpha }^{2} \: and \: { \beta }^{2} = > \\ {( \alpha + \beta )}^{2} - 2 \alpha \beta = { \alpha }^{2} + { \beta }^{2} \\ { \alpha }^{2} + { \beta }^{2} = {(4)}^{2} - 2(5) \\ { \alpha }^{2} - { \beta }^{2} = 6........(1) \\ \\ { \alpha }^{2} { \beta }^{2} = {5}^{2} = 25.........(2) \\ \\ {x}^{2} - (sum \: of \: roots)x + \\ (product \: of \: roots) \\ {x}^{2} - 6x + 25 = 0$