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