Jika a dan b akar-akar persamaan [tex] x^{2} + 5x - 3 = 0[/tex] , maka nilai dari [tex]a^{3} b^{2} + a^{2}b^{3}[/tex] adalah

x^2 + 5x + 3 = 0
a + b
= -b/a
= -5/1
= -5

ab
= c/a
= 3/1
= 3

a^3 b^2 + a^2 b^3
= a^2 b^2 (a + b)
= (ab)^2 (a + b)
= (3)^2 (-5)
= 9(-5)
= -45

Mapel : Matematika
Kelas : X SMA
Bab : Persamaan Kuadrat

Pembahasan :
x² + 5x - 3 = 0

Berdasarkan Teorema Vietta
a + b = -b/a
a + b = -5/1
a + b = -5

a . b = c/a
a . b = -3/1
a . b = -3

Maka...
a³b² + a²b³
= (ab)² (a + b)
= (-3)² (-5)
= 9(-5)
= -45