Question

Jika α dan β akar-akar persamaan kuadrat 4x² - 2x - 3 = 0, maka persamaan kuadrat yang akar-akarnya α + 1 dan β +1 adalah

Answer 1

X1 + X2 = -b/a = 2/4 = 1/2
X1.X2 = c/a = -3/4
α = α + 1
 β = β +1
α+β = α + 1 + β +1
       = α+ β + 2
       = 1/2 + 2 = 5/2
α.β = (α + 1)(β +1)
      = α.β  + 2(α+β) + 2
      = -3/4 + 2(1/2) + 2
      = 9/4
PKB ; x" - (α+β)x + α.β
        = x" - 5/2x + 9/4 (x4)
        = 4x" - 10x + 9

Answer 2

α + 1 = X1
β +1  = X2
α + β = -b/2a = -(-2)/2(4) = ¼
α β = c/a = -3/4

X² - (XI+X2)X + (X1.X2) = 0
X - ( α + 1+ β +1 )X + (( α + 1 )(β +1 )) = 0
X² - ( α + β +2)X + (α β + α + β +1 ) = 0
X² - (1/4 + 2)X + (-3/4 + ¼  + 1 ) = 0
X² – ( 9/4)X + ( ½ ) = 0    <DIKALIKAN 4 SEMUA>
4X² -9X + 2 =0