756° Вправа 756Алгебра 8 клас Тарасенкова 2025 · § 18 · стор. 226

756. Розв’яжіть квадратне рівняння:

1) ${\displaystyle x^2+4x-12=}$${\displaystyle 0}$;

${\displaystyle D=}$${\displaystyle 4^2-4\cdot 1\cdot (-12)=}$${\displaystyle 16+48=}$${\displaystyle 64}$;

${\displaystyle x_{1,2}=}$${\displaystyle \frac{-4\pm \sqrt{64}}{2\cdot 1}=}$${\displaystyle \frac{-4\pm 8}{2}}$;

${\displaystyle x_1=}$${\displaystyle \frac{-4+8}{2}=}$${\displaystyle 2}$;

${\displaystyle x_2=}$${\displaystyle \frac{-4-8}{2}=}$${\displaystyle -6}$;

2) ${\displaystyle x^2-3x-10=}$${\displaystyle 0}$;

${\displaystyle D=}$${\displaystyle {(-3)}^2-4\cdot 1\cdot (-10)=}$${\displaystyle 9+40=}$${\displaystyle 49}$;

${\displaystyle x_{1,2}=}$${\displaystyle \frac{3\pm \sqrt{49}}{2\cdot 1}=}$${\displaystyle \frac{3\pm 7}{2}}$;

${\displaystyle x_1=}$${\displaystyle \frac{3+7}{2}=}$${\displaystyle 5}$;

${\displaystyle x_2=}$${\displaystyle \frac{3-7}{2}=}$${\displaystyle -2}$;

3) ${\displaystyle x^2-6x+9=}$${\displaystyle 0}$;

${\displaystyle D=}$${\displaystyle {(-6)}^2-4\cdot 1\cdot 9=}$${\displaystyle 36-36=}$${\displaystyle 0}$;

${\displaystyle x=}$${\displaystyle \frac{6}{2}=}$${\displaystyle 3}$;

4) ${\displaystyle x^2+5x+8=}$${\displaystyle 0}$;

${\displaystyle D=}$${\displaystyle 5^2-4\cdot 1\cdot 8=}$${\displaystyle 25-32=}$${\displaystyle -7}$;

${\displaystyle D<0}$ — коренів немає;

5) ${\displaystyle x^2-5x+4=}$${\displaystyle 0}$;

${\displaystyle D=}$${\displaystyle {(-5)}^2-4\cdot 1\cdot 4=}$${\displaystyle 25-16=}$${\displaystyle 9}$;

${\displaystyle x_{1,2}=}$${\displaystyle \frac{5\pm \sqrt{9}}{2\cdot 1}=}$${\displaystyle \frac{5\pm 3}{2}}$;

${\displaystyle x_1=}$${\displaystyle \frac{5+3}{2}=}$${\displaystyle 4}$;

${\displaystyle x_2=}$${\displaystyle \frac{5-3}{2}=}$${\displaystyle 1}$;

6) ${\displaystyle x^2+6x+8=}$${\displaystyle 0}$;

${\displaystyle D=}$${\displaystyle 6^2-4\cdot 1\cdot 8=}$${\displaystyle 36-32=}$${\displaystyle 4}$;

${\displaystyle x_{1,2}=}$${\displaystyle \frac{-6\pm \sqrt{4}}{2\cdot 1}=}$${\displaystyle \frac{-6\pm 2}{2}}$;

${\displaystyle x_1=}$${\displaystyle \frac{-6+2}{2}=}$${\displaystyle -2}$;

${\displaystyle x_2=}$${\displaystyle \frac{-6-2}{2}=}$${\displaystyle -4}$;

7) ${\displaystyle x^2-x-6=}$${\displaystyle 0}$;

${\displaystyle D=}$${\displaystyle {(-1)}^2-4\cdot 1\cdot (-6)=}$${\displaystyle 1+24=}$${\displaystyle 25}$;

${\displaystyle x_{1,2}=}$${\displaystyle \frac{1\pm \sqrt{25}}{2\cdot 1}=}$${\displaystyle \frac{1\pm 5}{2}}$;

${\displaystyle x_1=}$${\displaystyle \frac{1+5}{2}=}$${\displaystyle 3}$;

${\displaystyle x_2=}$${\displaystyle \frac{1-5}{2}=}$${\displaystyle -2}$;

8) ${\displaystyle x^2-7x+10=}$${\displaystyle 0}$;

${\displaystyle D=}$${\displaystyle {(-7)}^2-4\cdot 1\cdot 10=}$${\displaystyle 49-40=}$${\displaystyle 9}$;

${\displaystyle x_{1,2}=}$${\displaystyle \frac{7\pm \sqrt{9}}{2\cdot 1}=}$${\displaystyle \frac{7\pm 3}{2}}$;

${\displaystyle x_1=}$${\displaystyle \frac{7+3}{2}=}$${\displaystyle 5}$;

${\displaystyle x_2=}$${\displaystyle \frac{7-3}{2}=}$${\displaystyle 2}$.