Question

1) Persamaan x^4+x^3-31x^2-x+30=0 mempunyai akar-akar x1,x2,x3,x4. jika x2 = -1 dan x4 = 5, maka nilai x1.x3 adalah...
2) Persamaan x^3+3x^2-2x+k=0 mempunyai dua akar yang berlawanan untuk nilai k =...

Answer 1

1) x1.x2.x3.x4 = e/a = 30
-1.5.x1.x3 = 30
-5.x1.x3 = 30
x1.x3 = 30/(-5) = -6

2) x1 = x1
x2 = -x1
x3 = x3
x1 + x2 + x3 = -3
x1 - x1 + x3 = -3
x3 = -3
x1.x2 + x1.x3 + x2.x3 = c/a = -2
x1.(-x1) + (-3)x1 + (-3)(-x1) = -2
-x1² - 3x1 + 3x1 = -2
-x1² = -2
x1² = 2
x1 = √2
x2 = -√2
sehingga nilai k
= -(x1.x2.x3) = -(-√2.√2.-3) = -6