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. Substitute the values of a, b, and c into the quadratic formula: x = \frac{-4 \pm \sqrt{4^2 - 4 \cdot 3 \cdot 1}}{2 \cdot 3}.
4. Calculate the discriminant, which is the expression under the square root: b^2 - 4ac = 16 - 12 = 4.
5. Simplify the expression: x = \frac{-4 \pm \sqrt{4}}{6}. Then, solve for the two possible values of x by considering both the positive and negative square roots.