jika x1 dan x2 adalah akar dari persamaan kuadrat [tex]2x {}^{2} - 4x - 3 = 0[/tex] maka nilai [tex]x1 {}^{2} - x2 {}^{2} [/tex] adalah...

2x² - 4x - 3 = 0
a = 2 ; b = -4 ; c = -3
D = b² - 4ac = 40

x1 + x2 = -b/a = 2
x1 . x2 = c/a = -3/2

x1 - x2 = √D /a = √10

x1² - x2²
= (x1 + x2)(x1 - x2)
= 2√10

Kelas 10 Matematika
Bab Persamaan dan Fungsi Kuadrat

2x² - 4x - 3 = 0
a = 2; b = -4; c = -3

x1 - x2
= +- (√b² - 4ac)/a
= +- (√((-4)² - 4 . 2 . (-3)))/2
= +- (√(16 + 24))/2
= +- (√40)/2
= +- (2/2) √10
= +- √10

Maka
x1² - x2²
= (x1 + x2) . (x1 - x2)
= (-b/a) . (+-√10)
= (-4/2) . (+-√10)
= -2 . (+-√10)
= 2√10
atau
= -2√10