Question

if alpha and beta are the root of equation x²-x+2=0 find the quadratic equation whose roots are alpha ²beta and alpha beta²​

Answer 1

Step-by-step explanation:

the value of

alpha = 1+√7i/2

beta =1-√7i/2

then our new equation is

Answer 2

Step-by-step explanation:

alpha+beta=1

& alpha*beta=2

quadratic equation=

$x {}^{2} - ( \alpha {}^{2} \beta + \alpha \beta {}^{2})x + \alpha {}^{2} \beta \times \alpha \beta {}^{2}$

=

$x {}^{2} - ( \alpha \beta \times \alpha + \beta )x + \alpha {}^{3} \beta {}^{3}$

$= x {}^{2} - (2 \times 1)x + 2 {}^{3}$

$= x {}^{2} - 2x + 8$