Jika x1 dan x2 adalah akar-akar persamaan kuadrat 2x - 8x + 4 = 0, hitunglah:

a. X1+ x2
b. X1.x2
c. x²1 + x ²2
d.x1/x2 + x2/x1

Jika x1 dan x2 adalah akar-akar persamaan kuadrat 2x – 8x + 4 = 0, hitunglah:

Penyelesaian:

Rumus:

$displaystyle boxed{begin{array}{l}text{Jika diketahui persamaan kuadrat } ax^2+bx+c=0text{ maka:} \ x_1+x_2 = -frac{b}{a} \ x_1cdot x_2 = frac{c}{a} end{array}}$

2x²–8x+4 = 0

jadi,

a = 2

b = -8

c = 4

a.)

$displaystyle begin{aligned} x_1+x_2 &= -frac{b}{a} \ &= -frac{-8}{2} \ &=;boxed{4}end{aligned}$

b.)

$displaystyle begin{aligned} x_1cdot x_2 &= frac{c}{a} \ &= frac{4}{2} \ &=;boxed{2} end{aligned}$

c.)

$displaystyle bold{PK:}\ boxed{(a+b)^2 = a^2+2ab+b^2} \ begin{aligned} x^2_1+x^2_2 &= (x_1+x_2)^2-2cdot x_1cdot x_2 \ &= (4)^2-2cdot2 \ &= 16-4 \ &=;boxed{12}end{aligned}$

d.)

$displaystyle bold{Pecahan:}\ boxed{frac{a}{b}+frac{c}{d} = frac{ad+cb}{bd}} \ begin{aligned} frac{x_1}{x_2}+frac{x_2}{x_1} &= frac{x_1^2+x_2^2}{x_1cdot x_2} \ &= frac{12}{2} \ &=;boxed{6}end{aligned}$