Question

se rezolva aecuatiile cu formula delta de gradul II

Answer 1

1. $x^{2} -3x+2=0$

Identificăm coeficienții: a=1 b=-3 c=2;

Calculăm Δ

Δ$={b^{2} -4*ac}$

Δ=${(-3)^{2} -4 *1*2}=9-8=1$

Aflăm $x_{1} , x_{2}.$

$x_{1} =\frac{-b+ \sqrt{delta} }{2*a}=\frac{3+1}{2*1} =\frac{4}{2} =2\\\\x_{2} =\frac{-b- \sqrt{delta} }{2*a}=\frac{3-1}{2*1} =\frac{-2}{2} =1$

S={1;2}

2. $x^{2} -5x+6=0$

Identificăm coeficienții: a=1 b=-5, c=6;

Calculăm Δ

Δ=$={b^{2} -4*ac}$

Δ=${(-5)^{2} -4 *1*6}=25-24=1$

$x_{1} =\frac{-b+ \sqrt{delta} }{2*a}=\frac{5+1}{2*1} =\frac{6}{2} =3\\\\\\x_{2} =\frac{-b- \sqrt{delta} }{2*a}=\frac{5-1}{2*1} =\frac{4}{2} =2$

S={2;3}

3. $x^{2} -9x+20=0$

Identificăm coeficienții: a=1 b=-9, c=20;

Calculăm Δ

Δ$={b^{2} -4*ac}$

Δ=${(-9)^{2} -4 *1*20}=81-80=1$

$x_{1} =\frac{-b+ \sqrt{delta} }{2*a}=\frac{9+1}{2*1} =\frac{10}{2} =5\\\\\\x_{2} =\frac{-b- \sqrt{delta} }{2*a}=\frac{9-1}{2*1} =\frac{8}{2} =4$

S={4;5} 

4. $x^{2} +5x+6=0$

Identificăm coeficienții: a=1 b=5, c=6;

Calculăm Δ

Δ$={b^{2} -4*ac}$

Δ$={(5)^{2} -4 *1*6}=25-24=1$

$x_{1} =\frac{-b+ \sqrt{delta} }{2*a}=\frac{-5+1}{2*1} =\frac{-4}{2} =-2\\\\\\\\x_{2} =\frac{-b- \sqrt{delta} }{2*a}=\frac{-5-1}{2*1} =\frac{-6}{2} =-3$

S={-3;-2}