Answer: Two distinct real roots.
Step-by-step explanation:
To solve this problem you must find the discriminant of the quadratic equation with the following formula:
[tex]D=b^2-4ac[/tex]
Given the quadratic equation [tex]0=5x^2+2x-12[/tex], you have that:
[tex]a=5\\b=2\\c=-12[/tex]
When you subsitute values into the formula, you obtain the following result:
[tex]D=(2)^2-4(5)(-12)[/tex]
[tex]D=244[/tex]
Therefore, as [tex]D>0[/tex] then you can conclude that the equation has two distinct real roots.