Answer:
roots are real and distinct
Step-by-step explanation:
To determine the nature of the roots use the discriminant , b² - 4ac
• If b² - 4ac > 0 then 2 real and distinct roots
• If b² - 4ac = 0 then 2 real and equal roots
• If b² - 4ac < 0 then roots are not real
Given
2x² - [tex]\sqrt{5}[/tex] x - 2 = 0
with a = 2, b = - [tex]\sqrt{5}[/tex] , c = - 2 , then
b² - 4ac
= (- [tex]\sqrt{5}[/tex] )² - ( 4 × 2 × - 2)
= 5 - (- 16)
= 5 + 16
= 21
Since b² - 4ac > 0 then the equation has 2 real and distinct roots
