Question

Calculati discriminantul ecuatiei; determinati daca ecuatia are solutii in R si aflati solutiile in cazul in care ele exista:
a)x²-7x-18=0 b)3x²-5x+2=0 c)3x²-11x+10=0
d)4x²-4x+1=0 e)x²+3x+5=0 f)2x-x²+3=0
g)1-x-6x²=0 h)25x²+10x+1=0 i)x²+7x-1=0

Answer 1

x²-7x-18=0;  x²-9x+2x-18=0;  x(x-9)+2(x-9)=0;  (x+2)(x-9)=0; x=-2,x=9

3x²-5x+2=0;  3x²-3x-2x+2=0; 3x(x-1)-2(x-1)=0; (3x-2)(x-1)=0 x=2/3,x=1

3x²-11x+10=0;  3x²-6x-5x+10=0;  3x(x-2)-5(x-2)=0; (3x-5)(x-2)=0 x=5/3, x=2

4x²-4x+1=0;  4x²-2x-2x+1=0;  2x(2x-1)-(2x-1)=0;  (2x-1)(2x-1)=0   x=1/2
 
2x-x²+3=0;   3x-x-x²+3=0;  3(x+1)-x(1+x)=0;  (x+1)(3-x)=0   x=-1, x=3

1-x-6x²=0;   1-3x+2x-6x²=0; (1-3x)+2x(1-3x)=0;  (1-3x)(1+2x)=0  x=1/3, x=-1/2

25x²+10x+1=0;  25x²+5x+5x+1=0;  5x(5x+1)+(5x+1)=0; (5x+1)^2=0  x=1/5