To solve the quadratic equation 3x^2 + x - 5 = 0, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this equation, a, b, and c represent the coefficients of the quadratic equation.
For the given equation, the coefficients are:
a = 3
b = 1
c = -5
Substituting these values into the quadratic formula, we get:
x = (-(1) ± √((1)^2 - 4(3)(-5))) / (2(3))
Simplifying further:
x = (-1 ± √(1 + 60)) / 6
x = (-1 ± √61) / 6
Now, we can calculate the two solutions:
x₁ = (-1 + √61) / 6 ≈ 0.83 (rounded to 2 decimal places)
x₂ = (-1 - √61) / 6 ≈ -1.50 (rounded to 2 decimal places)
Therefore, the solutions to the quadratic equation 3x^2 + x - 5 = 0, rounded to 2 decimal places, are approximately:
x₁ ≈ 0.83
x₂ ≈ -1.50