Answer:
The correct option is 2 and the solutions of given equation are irrational.
Step-by-step explanation:
The given equation is
[tex]3x^2-x-5=0[/tex]
If an equation is defined as
[tex]ax^2+bx+c=0[/tex]
Then the quadratic formula is
[tex]x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
The value of discriminant for the given equation is
[tex]x=\frac{-(-1)\pm \sqrt{(-1)^2-4(3)(-5)}}{2(3)}[/tex]
[tex]x=\frac{1\pm \sqrt{61}}{6}[/tex]
Since [tex]\sqrt{61}[/tex] is an irrational number, therefore the addition and division with an irrational number is irrational.
So, both the solutions of given equation are irrational and option 2 is correct.
