0. Review of College Algebra

Solving Quadratic Equations

0. Review of College Algebra

Solving Quadratic Equations

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Multiple Choice

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

$x=3,x=-1$

$x=-\frac13,x=-1$

$x=-3,x=-1$

$x=\frac13,x=-1$

Verified step by step guidance

Identify the coefficients in the quadratic equation 3x^2 + 4x + 1 = 0. Here, a = 3, b = 4, and c = 1.

Recall the quadratic formula: x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}. This formula is used to find the roots of a quadratic equation ax^2 + bx + c = 0.

Substitute the identified coefficients into the quadratic formula: x = \frac{-4 \pm \sqrt{4^2 - 4 \cdot 3 \cdot 1}}{2 \cdot 3}.

Calculate the discriminant, which is the expression under the square root: b^2 - 4ac = 4^2 - 4 \cdot 3 \cdot 1. Simplify this to find the value of the discriminant.

Use the value of the discriminant to determine the roots by completing the calculation in the quadratic formula: x = \frac{-4 \pm \sqrt{discriminant}}{6}. Simplify to find the two possible values for x.