Question

Solve question 20
please​

Answer 1

Answer:

(i). x² - 6x + 11 ; (ii) 3x² - 2x + 1

Step-by-step explanation:

If α and β are zeros of f(x) = ax² + bx + c , then

α + β = - $\frac{b}{a}$

α × β = $\frac{c}{a}$

~~~~~~~~~~~~

f(x) = x² - 2x + 3

D = (- 2)² - 12 = - 8

α = (2 - 2i√2) / 2 = 1 - i√2

β = 1 + i√2

(i) $x_{1}$ = 1 - i√2 + 2 = 3 - i√2

$x_{2}$ = 3 + i√2

$x_{1}$ + $x_{2}$ = 6

$x_{1}$$x_{2}$ = (3 - i√2)(3 + i√2) = 9 - 2(- 1) = 11

g(x) = x² - 6x + 11

(ii) $x_{1}$ = (1 - i√2 - 1) / (1 - i√2 + 1) = - i√2 / 2 - i√2 = (1 - i√2) / 3

$x_{2}$ = (1 + i√2) / 3

$x_{1}$ + $x_{2}$ = 2 / 3

$x_{1}$$x_{2}$ = 1 / 3

h(x) = 3x² - 2x + 1