Question

-0,5x²+6x-7=0
-x²-5x+6=0
5x²-8x-4=0
Решить через дискриминант.

Answer 1

$1) -0,5 x^2 +6 x -7=0 \a= -0,5; b=6; c=-7; \D=b^2-4ac \D= 36 = 6^2\x_{1}=frac{ -6-sqrt{ 36 }}{ 2*-0,5 } = frac{ -6-6 }{ -1 }= 12;\\x_{2}=frac{ -6+sqrt{ 36 }}{ 2*-0,5 } = frac{ -6+6 }{ -1 }= 0;$

$2) -x^2 -5 x +6=0 \a= -1; b=-5; c=+6; \D=b^2-4ac \D= 49 = 7^2\x_{1}=frac{ +5-sqrt{ 49 }}{ 2*-1 } = frac{ +5-7 }{ -2 }=1;\\x_{2}=frac{ +5+sqrt{ 49 }}{ 2*-1 } = frac{ +5+7 }{ -2 }=-6;$

$3) 5 x^2 -8 x -4=0 \a= 5; b=-8; c=-4; \D=b^2-4ac \D= 144 = 12^2\x_{1}=frac{ +8-sqrt{ 144 }}{ 2*5 } = frac{ +8-12 }{ 10 }=-0.4;\\x_{2}=frac{ +8+sqrt{ 144 }}{ 2*5 } = frac{ +8+12 }{ 10 }=2;$