788° Вправа 788Алгебра 8 клас Тарасенкова 2025 · § 19 · стор. 235

788. Скориставшись теоремою Вієта, розв’яжіть квадратне рівняння:

1) ${\displaystyle x^2+8x-9=}$${\displaystyle 0}$;

${\displaystyle x_1+x_2=}$${\displaystyle -8}$; ${\displaystyle x_1\cdot x_2=}$${\displaystyle -9}$;

${\displaystyle x_1=}$${\displaystyle -9}$; ${\displaystyle x_2=}$${\displaystyle 1}$;

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

${\displaystyle x_1+x_2=}$${\displaystyle 3}$; ${\displaystyle x_1\cdot x_2=}$${\displaystyle -10}$;

${\displaystyle x_1=}$${\displaystyle -2}$; ${\displaystyle x_2=}$${\displaystyle 5}$;

3) ${\displaystyle x^2-9x+20=}$${\displaystyle 0}$;

${\displaystyle x_1+x_2=}$${\displaystyle 9}$; ${\displaystyle x_1\cdot x_2=}$${\displaystyle 20}$;

${\displaystyle x_1=}$${\displaystyle 4}$; ${\displaystyle x_2=}$${\displaystyle 5}$;

4) ${\displaystyle x^2+9x+8=}$${\displaystyle 0}$;

${\displaystyle x_1+x_2=}$${\displaystyle -9}$; ${\displaystyle x_1\cdot x_2=}$${\displaystyle 8}$;

${\displaystyle x_1=}$${\displaystyle -8}$; ${\displaystyle x_2=}$${\displaystyle -1}$;

5) ${\displaystyle x^2-5x-14=}$${\displaystyle 0}$;

${\displaystyle x_1+x_2=}$${\displaystyle 5}$; ${\displaystyle x_1\cdot x_2=}$${\displaystyle -14}$;

${\displaystyle x_1=}$${\displaystyle -2}$; ${\displaystyle x_2=}$${\displaystyle 7}$;

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

${\displaystyle x_1+x_2=}$${\displaystyle -6}$; ${\displaystyle x_1\cdot x_2=}$${\displaystyle 8}$;

${\displaystyle x_1=}$${\displaystyle -4}$; ${\displaystyle x_2=}$${\displaystyle -2}$;

7) ${\displaystyle x^2-x-20=}$${\displaystyle 0}$;

${\displaystyle x_1+x_2=}$${\displaystyle 1}$; ${\displaystyle x_1\cdot x_2=}$${\displaystyle -20}$;

${\displaystyle x_1=}$${\displaystyle -4}$; ${\displaystyle x_2=}$${\displaystyle 5}$;

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

${\displaystyle x_1+x_2=}$${\displaystyle 7}$; ${\displaystyle x_1\cdot x_2=}$${\displaystyle 10}$;

${\displaystyle x_1=}$${\displaystyle 2}$; ${\displaystyle x_2=}$${\displaystyle 5}$.