Solve the given quadratic equation using the quadratic formula. $3x^2+4x+1=0$

• A. $x=3,x=-1$
• B. $x=-\frac13,x=-1$
• C. $x=-3,x=-1$
• D. $x=\frac13,x=-1$

Answer: (B)

Verified step by step guidance

1. Identify the coefficients from the quadratic equation 3x^2 + 4x + 1 = 0. Here, a = 3, b = 4, and c = 1.
2. Recall the quadratic formula: x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}. This formula is used to find the roots of any quadratic equation ax^2 + bx + c = 0.
3. Calculate the discriminant, which is the expression under the square root in the quadratic formula: b^2 - 4ac. Substitute the values: 4^2 - 4(3)(1).
4. Evaluate the discriminant to determine the nature of the roots. If the discriminant is positive, there are two distinct real roots; if zero, one real root; if negative, two complex roots.
5. Substitute the values of a, b, and the calculated discriminant into the quadratic formula to find the values of x. Simplify the expression to get the roots of the equation.