959 Вправа 959Алгебра 8 клас Бевз 2025 · § 19 · стор. 183

959. Користуючись формулою коренів, розв’яжи рівняння. а) 2x² − 7x − 30 = 0; б) 4x² + 3x − 10 = 0; в) 3y² − 7y + 4 = 0; г) 5x² + 7x + 2 = 0.

а) ${\displaystyle 2x^2-7x-30=}$${\displaystyle 0}$;

${\displaystyle a=}$${\displaystyle 2,b=}$${\displaystyle -7,c=}$${\displaystyle -30}$;

${\displaystyle D=}$${\displaystyle b^2-4ac=}$${\displaystyle {(-7)}^2-4\cdot 2\cdot (-30)=}$${\displaystyle 49+240=}$${\displaystyle 289}$;

${\displaystyle D>0}$, два корені:

${\displaystyle x_{1,2}=}$${\displaystyle \frac{-b\pm \sqrt{D}}{2a}=}$${\displaystyle \frac{7\pm \sqrt{289}}{4}=}$${\displaystyle \frac{7\pm 17}{4}}$;

${\displaystyle x_1=}$${\displaystyle \frac{7+17}{4}=}$${\displaystyle 6}$;

${\displaystyle x_2=}$${\displaystyle \frac{7-17}{4}=}$${\displaystyle -2,5}$;

б) ${\displaystyle 4x^2+3x-10=}$${\displaystyle 0}$;

${\displaystyle a=}$${\displaystyle 4,b=}$${\displaystyle 3,c=}$${\displaystyle -10}$;

${\displaystyle D=}$${\displaystyle b^2-4ac=}$${\displaystyle 3^2-4\cdot 4\cdot (-10)=}$${\displaystyle 9+160=}$${\displaystyle 169}$;

${\displaystyle D>0}$, два корені:

${\displaystyle x_{1,2}=}$${\displaystyle \frac{-b\pm \sqrt{D}}{2a}=}$${\displaystyle \frac{-3\pm \sqrt{169}}{8}=}$${\displaystyle \frac{-3\pm 13}{8}}$;

${\displaystyle x_1=}$${\displaystyle \frac{-3+13}{8}=}$${\displaystyle 1,25}$;

${\displaystyle x_2=}$${\displaystyle \frac{-3-13}{8}=}$${\displaystyle -2}$;

в) ${\displaystyle 3y^2-7y+4=}$${\displaystyle 0}$;

${\displaystyle a=}$${\displaystyle 3,b=}$${\displaystyle -7,c=}$${\displaystyle 4}$;

${\displaystyle D=}$${\displaystyle b^2-4ac=}$${\displaystyle {(-7)}^2-4\cdot 3\cdot 4=}$${\displaystyle 49-48=}$${\displaystyle 1}$;

${\displaystyle D>0}$, два корені:

${\displaystyle y_{1,2}=}$${\displaystyle \frac{-b\pm \sqrt{D}}{2a}=}$${\displaystyle \frac{7\pm \sqrt{1}}{6}=}$${\displaystyle \frac{7\pm 1}{6}}$;

${\displaystyle y_1=}$${\displaystyle \frac{7+1}{6}=}$${\displaystyle \frac{4}{3}}$;

${\displaystyle y_2=}$${\displaystyle \frac{7-1}{6}=}$${\displaystyle 1}$;

г) ${\displaystyle 5x^2+7x+2=}$${\displaystyle 0}$;

${\displaystyle a=}$${\displaystyle 5,b=}$${\displaystyle 7,c=}$${\displaystyle 2}$;

${\displaystyle D=}$${\displaystyle b^2-4ac=}$${\displaystyle 7^2-4\cdot 5\cdot 2=}$${\displaystyle 49-40=}$${\displaystyle 9}$;

${\displaystyle D>0}$, два корені:

${\displaystyle x_{1,2}=}$${\displaystyle \frac{-b\pm \sqrt{D}}{2a}=}$${\displaystyle \frac{-7\pm \sqrt{9}}{10}=}$${\displaystyle \frac{-7\pm 3}{10}}$;

${\displaystyle x_1=}$${\displaystyle \frac{-7+3}{10}=}$${\displaystyle -0,4}$;

${\displaystyle x_2=}$${\displaystyle \frac{-7-3}{10}=}$${\displaystyle -1}$.