Розділ 3. КВАДРАТНІ РІВНЯННЯ » 24.9 (1-3)

24.9 Розкладіть на множники квадратний тричлен: 1) x² – 5x + 4. D = (–5)² – 4 • 4 = 9; x1 = (5+3)/(2 ) = 5; x2 = (5-3)/2 = 1; x² – 5x + 4 = (x – 4)(x – 1). 2) x² + 7x – 8. D = 72 – 4 • (–8) = 81; x1 = (-7+9)/(2 ) = 1; x2 = (-7-9)/2 = –8; x² + 7x – 8 = (x – 1)(x + 8). 3) 2x² – 5x + 2. D = (–5)² – 4 • 2 • 2 = 9; x1 = (5+3)/4 = 2; x2 = (5-3)/4 = 1/2; 2x² – 5x + 2 = 2(x – 2)(x – 1/2) = (x – 2)(2x – 1).