Final answer:
To find the roots of 3x^2 - 11x - 4 = 0, we can apply the quadratic formula, obtaining two solutions: x = 4 and x = -1/3.
Step-by-step explanation:
To find the roots of the quadratic equation 3x^2 - 11x - 4 = 0, we can use the quadratic formula. Quadratic equations have the form ax^2 + bx + c = 0, where a, b, and c are constants and x represents the variable. The quadratic formula is given by:
Quadratic Formula
x = (-b ± √(b^2 - 4ac)) / (2a)
For your equation, a = 3, b = -11, and c = -4. Substituting these values into the quadratic formula, we get the following calculations:
x = (-(-11) ± √((-11)^2 - 4*3*(-4))) / (2*3)
x = (11 ± √(121 + 48)) / 6
x = (11 ± √(169)) / 6
x = (11 ± 13) / 6
This results in two possible solutions for x:
- x = (11 + 13) / 6 = 24 / 6 = 4
- x = (11 - 13) / 6 = -2 / 6 = -1/3
Thus, the roots of the equation 3x^2 - 11x - 4 = 0 are x = 4 and x = -1/3.