Question

pls answer very important ​

Answer 1

$\huge\underbrace\purple{\dag Solution \dag}$

See the pic that I have attached

Answer 2

Answer:

$k( {x}^{2} - 5x + 156)$

Step-by-step explanation:

given,

$f(x) = x^{2} - x - 6$

since,

$\alpha \: and \: \beta \: are \: the \: zeros$

$\alpha + \beta = 1$

and

$\alpha \beta = 6$

now zeros of required polynomial r(x) are

$3 \alpha + 2 \beta \: and \: 2 \alpha + 3 \beta$

therefore, sum =

$5 \alpha + 5 \beta \\ = 5( \alpha + \beta ) \\ = 5(1) \\ = 5$

also, product =

$6 { \alpha }^{2} + 9 \alpha \beta + 4 \alpha \beta + 6 { \beta }^{2} \\ = 6( { \alpha }^{2} + \beta {}^{2} ) + 13 \alpha \beta \\ = 6(1) {}^{2} + 12(6) + 13(6) \\ = 6 + 72 + 78 = 156$

therefore the required polynomial is

r(x) =

$k ({x}^{2} - 5x + 156)$

Hope this helps :)