Question

Jika x1 dan x1 akar akar persamaan ax^+bx+c=0, maka persamaan kuadrat yang akar akarnya x1+x2 dan x1*x2 adalah

Answer 1

Ax² + bx + c = 0
x1+x2 = -b/a
x1x2 = c/a

maka pers kuadrat yg akar-akarnya (x1+x2) dan x1x2 adalh :
x² - (x1+x2)x + x1x2 = 0
x² - (-b/a)x + c/a = 0
x² + b/a x + c/a = 0  (kedua ruas dikali dg a)
ax² + bx + c = 0
(it seems back to original equation :v)

Answer 2

X1+x2 = -b/a
x1*x2 = c/a
akar-akar baru
(x1+x2) + (x1*x2) = -b/a + c/a = (c-b)/a
(x1+x2)*(x1*x2) = -b/a * c/a = -bc/a^2
persamaan kuadrat baru