Penjelasan dengan langkah-langkah:

Persamaan kuadrat.

ax² + bx + c = 0

x₁ + x₂ = -b/a

x₁ . x₂ = c/a

Pk lama .

2x² - 5x + 1 = 0

a = 2

b = -5

c = 1

x₁ + x₂ = 5/2

x₁ . x₂ = 1/2

Pk baru ;

A = x₁ - 1

B = x₂ - 1

A + B = x₁ - 1 + x₂ - 1

. = x₁ + x₂ - 2

. = 5/2 - 2

. = 1/2

A . B = ( x₁ - 1 ) ( x₂ - 1 )

. = x₁ . x₂ - x₁ - x₂ + 1

. = x₁ . x₂ - ( x₁ + x₂ ) + 1

. = 1/2 - ( 5/2 ) + 1

. = 1/2 - 5/2 + 2/2

. = -2/2

. = -1

pk baru.

x² - ( A + B ) x + ( A . B ) = 0

x² - ( 1/2 ) x + ( -1 ) = 0

x² - 1/2 x - 1 = 0

2x² - x - 2 = 0 ----------> dikalikan 2

atau pakai cara invers.

( x - 1 ) -------> iversnya ( x + 1 ).

subtitusi ( x + 1 ) ke pk lama.

2( x + 1 )² - 5 ( x + 1 ) + 1 = 0

2 ( x² + 2x + 1 ) - 5x - 5 + 1 = 0

2x² + 4x + 2 - 5x - 5 + 1 = 0

2x² - x - 2 = 0

opsi pilihan ( E )

semoga bisa membantu