Question

Имеет ли квадратный трёхчлен корни, если имеет, то какие?
1) 10х2+5х+5
2) с2-2с-4
3) -2у+12у-18
4) 12x2-12

Answer 1

$1) \ 10x^{2}+5x+5=0\\\\2x^{2}+x+1=0\\\\D=1^{2} -4\cdot2\cdot1=1-8=-7<0- \boxed{\ kornei \ net}\\\\\\2)c^{2} -2c-4=0\\\\D=(-2)^{2} -4\cdot(-4)=4+16=20=(2\sqrt{5})^{2}\\\\c_{1} =\dfrac{2+2\sqrt{5} }{2}=1+\sqrt{5}\\\\c_{2} =\dfrac{2-2\sqrt{5} }{2}=1-\sqrt{5}\\\\\boxed{c_{1} =1+\sqrt{5} \ ; \ c_{2}=1-\sqrt{5} }$

$3) \ -2y^{2}+12y-18=0\\\\y^{2}-6y+9=0\\\\(y-3)^{2} =0\\\\y-3=0\\\\\boxed{y=3}\\\\\\4) \ 12x^{2} -12=0\\\\x^{2}-1=0 \\\\(x-1)(x+1)=0\\\\x-1=0 \ \Rightarrow \ \boxed{x_{1} =1}\\\\x+1=0 \ \Rightarrow \ \boxed{x_{2}=-1 }$