Answer:
2
Step-by-step explanation:
To find how many real solution a quadratic equation has, we just need to find the value of its discriminant. If the discriminant is zero, the quadratic only has one real solution; if the discriminant is positive, the quadratic has two real solution; if the discriminate is negative, the quadratic doesn't has any real solutions.
The discriminant of a quadratic equation of the form [tex]ax^2+bx+c[/tex] is given by: [tex]b^2-4ac[/tex]
We know from our quadratic that [tex]a=3[/tex], [tex]b=-5[/tex], and [tex]c=-5[/tex].
Replacing values:
[tex](-5)^2-4(3)(-5)[/tex]
[tex]25+60[/tex]
[tex]85[/tex]
Since the discriminant is positive, we can conclude that our quadratic equation has two real solutions.
