Answer:
0 solution
Step-by-step explanation:
Given
[tex]x^2 + 5x+ 7 = 0[/tex]
Required
Find number of solutions;
The number of solutions can be determined via the value of determinants, D;
Such that
[tex]D = {b^2} - {4ac}[/tex]
By comparing the general form of equation;
[tex]ax^2 +bc x + c = 0[/tex]
with [tex]x^2 + 5x+ 7 = 0[/tex]
This gives
[tex]a = 1\\b = 5\\c = 7[/tex]
So;
[tex]D = {b^2} - {4ac}[/tex] becomes
[tex]D = {5^2} - {4*1*7}[/tex]
[tex]D = {25} - {28}[/tex]
[tex]D = -3[/tex]
The calculated value of D is less than 0;
This implies that [tex]x^2 + 5x+ 7 = 0[/tex] has no real solution
