Question

Determine the type and number of solutions of 7x^2+3x+8=0

Answer 1

`7x^2+3x+8=0\\\\ \Delta=3^2-4\cdot7\cdot8=9-224=-115\ \ \Rightarrow\ \ \ no\ real\ solution\\\\\ two\ complex\ solutions\\\\\Delta=-115=115\cdot i^2\ \ \ \Rightarrow\ \ \ √(\Delta) = √(115)\ i\\\\x_1= (-b- √(\Delta) )/(2a) = (-3- √(115)\ i)/(2\cdot 7) = (-3- √(115i))/(14)\\\\x_2= (-b+ √(\Delta) )/(2a) = (-3+ √(115)\ i)/(2\cdot 7) = (-3+ √(115)\ i)/(14)`

Answer 2

`7x^2+3x+8=0 \\ \\a =7, \ b=3 ,\ c=8 \\ \\\Delta =b^2 - 4ac = 3^2 -4\cdot 7\cdot 8=9-224=-215\\ \\ Answer : \ \Delta \ is \ negative,\ this \ gives \ two \ imaginary \ solutions`