Solve 3x^2+2x+1
Solve ax² + bx + c = 0 using the quadratic formula with discriminant analysis.
3x2+2x+1
Solve using the quadratic formula since this quadratic does not factor nicely:
Compare with the standard form ax² + bx + c = 0:
a = 3, b = 2, c = 1
x = (−b ± √b2 − 4ac) / 2a
x = (-2 ± √(2)2 − 4(3)(1)) / 2(3)
x = (-2 ± √4 − 12) / 6
x = (-2 ± √-8) / 6
Δ = b² − 4ac = 4 − 12 = -8
Since Δ = -8 is negative, the solutions are complex:
x = (-1 ± i√2) / 3
x = (-1 ± i√2) / 3
How to solve 3x^2+2x+1
To solve 3x^2+2x+1, we can try factoring, use the quadratic formula, or complete the square. The solution is x = (-1 ± i√2) / 3.
This is a second-degree quadratic equation — the highest power of the variable is 2. Quadratic equations can have two real roots, one repeated root, or two complex roots.
Frequently asked questions
What is the answer to 3x^2+2x+1?
The answer is x = (-1 ± i√2) / 3.
What method is used?
factoring when possible, or the quadratic formula x = (−b ± √(b²−4ac)) / 2a. The discriminant b²−4ac determines the number and type of solutions.
How do I verify this?
Substituting the solution(s) back into 3x^2+2x+1 confirms both sides are equal.