746' Вправа 746Алгебра 8 клас Тарасенкова 2025 · § 18 · стор. 224

746. Які з чисел 0; 1; –1; –0,5; 0,2; 2 є коренями квадратного рівняння:

1) ${\displaystyle x^2-x-2=}$${\displaystyle 0}$:

${\displaystyle x=}$${\displaystyle 0}$: ${\displaystyle 0^2-0-2=}$${\displaystyle -2}$; ${\displaystyle -2\ne 0}$ — ні;

${\displaystyle x=}$${\displaystyle 1}$: ${\displaystyle 1^2-1-2=}$${\displaystyle -2}$; ${\displaystyle -2\ne 0}$ — ні;

${\displaystyle x=}$${\displaystyle -1}$: ${\displaystyle {(-1)}^2-(-1)-2=}$${\displaystyle 1+1-2=}$${\displaystyle 0}$; ${\displaystyle 0=}$${\displaystyle 0}$ — так;

${\displaystyle x=}$${\displaystyle -0,5}$: ${\displaystyle {(-0,5)}^2-(-0,5)-2=}$${\displaystyle 0,25+0,5-2=}$${\displaystyle -1,25}$; ${\displaystyle -1,25\ne 0}$ — ні;

${\displaystyle x=}$${\displaystyle 0,2}$: ${\displaystyle {0,2}^2-0,2-2=}$${\displaystyle 0,04-0,2-2=}$${\displaystyle -2,16}$; ${\displaystyle -2,16\ne 0}$ — ні;

${\displaystyle x=}$${\displaystyle 2}$: ${\displaystyle 2^2-2-2=}$${\displaystyle 4-2-2=}$${\displaystyle 0}$; ${\displaystyle 0=}$${\displaystyle 0}$ — так;

корені: ${\displaystyle -1}$ і ${\displaystyle 2}$;

2) ${\displaystyle 2x^2+x=}$${\displaystyle 0}$:

${\displaystyle x=}$${\displaystyle 0}$: ${\displaystyle 2\cdot 0^2+0=}$${\displaystyle 0}$; ${\displaystyle 0=}$${\displaystyle 0}$ — так;

${\displaystyle x=}$${\displaystyle 1}$: ${\displaystyle 2\cdot 1^2+1=}$${\displaystyle 3}$; ${\displaystyle 3\ne 0}$ — ні;

${\displaystyle x=}$${\displaystyle -1}$: ${\displaystyle 2\cdot {(-1)}^2+(-1)=}$${\displaystyle 2-1=}$${\displaystyle 1}$; ${\displaystyle 1\ne 0}$ — ні;

${\displaystyle x=}$${\displaystyle -0,5}$: ${\displaystyle 2\cdot {(-0,5)}^2+(-0,5)=}$${\displaystyle 2\cdot 0,25-0,5=}$${\displaystyle 0,5-0,5=}$${\displaystyle 0}$; ${\displaystyle 0=}$${\displaystyle 0}$ — так;

${\displaystyle x=}$${\displaystyle 0,2}$: ${\displaystyle 2\cdot {0,2}^2+0,2=}$${\displaystyle 2\cdot 0,04+0,2=}$${\displaystyle 0,08+0,2=}$${\displaystyle 0,28}$; ${\displaystyle 0,28\ne 0}$ — ні;

${\displaystyle x=}$${\displaystyle 2}$: ${\displaystyle 2\cdot 2^2+2=}$${\displaystyle 2\cdot 4+2=}$${\displaystyle 10}$; ${\displaystyle 10\ne 0}$ — ні;

корені: ${\displaystyle 0}$ і ${\displaystyle -0,5}$.