Cześć!
a)
[tex]2x^2+7x+3=0\\\\a=2, \ b=7, \ c=3\\\\\Delta=7^2-4\cdot2\cdot3=49-24=25\\\\\sqrt{\Delta}=\sqrt{25}=5\\\\x_1=\frac{-7-5}{2\cdot2}=\frac{-12}{4}=-3\\\\x_2=\frac{-7+5}{2\cdot2}=\frac{-2}{4}=-\frac{1}{2}[/tex]
b)
[tex]4x^2-x-5=0\\\\a=4, \ b=-1, \ c=-5\\\\\Delta=(-1)^2-4\cdot4\cdot(-5)=1+80=81\\\\\sqrt{\Delta}=\sqrt{81}=9\\\\x_1=\frac{-(-1)-9}{2\cdot4}=\frac{1-9}{8}=\frac{-8}{8}=-1\\\\x_2=\frac{-(-1)+9}{2\cdot4}=\frac{1+9}{8}=\frac{10}{8}=1,25[/tex]
c)
[tex]3x^2-5x-2=0\\\\a=3, \ b=-5, \ c=-2\\\\\Delta=(-5)^2-4\cdot3\cdot(-2)=25+24=49\\\\\sqrt{\Delta}=\sqrt{49}=7\\\\x_1=\frac{-(-5)-7}{2\cdot3}=\frac{5-7}{6}=\frac{-2}{6}=-\frac{1}{3}\\\\x_2=\frac{-(-5)+7}{2\cdot3}=\frac{5+7}{6}=\frac{12}{6}=2[/tex]
Odpowiedź:
Szczegółowe wyjaśnienie:
Δ=b² -4ac
x1= -b-√Δ /2a
x2=- b+√Δ /2a
2x²+7x+3=0
Δ=7²-4*2*3=49 -24=25
√Δ=√25=5
x1= -7-5/2*2=-12/4 = -3
x2= -7+5/2*2=-2/4= -1/2
4x² -x-5=0
Δ=(-1)²-4*4*(-5)=1+80=81
√Δ=√81=9
x1= -(-1) -9/2*4=-8/8= -1
x2= -(-1)+9/2*4=10/8=5/4=1 1/4
3x² -5x-2=0
Δ=(-5)²-4*3*(-2)=25+24=49
√Δ=49=7
x1= -(-5)- 7/2*3=-2/6= -1/3
x2=-(-5)+7/2*3=12/6=2