Question

Susunlah persamaan berikut jika akar akarnya adalah:
a. -4 dan -3
b. 2/3 dan -3/5
c. p dan q
d. 1/(alfa) dan 1/(beta)

Answer 1

1)x1 +x2 = -4 + -3 = -7
x1 x2= (-4)(-3)= 12
PK --> x^2 + 7x +12  = 0
.
2)
x1 + x2 = 2/3 - 3/5 = 1/15
x1x2 = (2/3)(-3/5)= -2/5
PH --> x^2 - 1/15 x - 2/5 = 0
atau 15 x^2 - x - 6 = 0
.
3)
x1+x2= p+q
x1x2 = pq
PK --> x^2 - (p+q) + (pq) = 0
.
4)
x1+x2 = 1/a + 1/b = (a+b)/(ab)
x1x2 = 1/a. 1/b = 1/(ab)
PH --> x^2 - (a+b)/(ab) x + 1/ab = 0
(ab) x^2 - (a+b) x + 1 = 0