Solve 3x^2+12x+9
Solve ax² + bx + c = 0 using the quadratic formula with discriminant analysis.
3x2+12x+9
Solve by factoring the quadratic and applying the zero product property:
Divide everything by 3:
x2 + 4x + 3 = 0
We need two numbers that multiply to 3 (the constant term) and add to 4 (the coefficient of x):
3 × 1 = 3 and 3 + 1 = 4
Write the factored form using these numbers:
(x + 1)(x + 3) = 0
If a product equals zero, at least one of the factors must be zero. Set each factor equal to zero and solve:
x + 1 = 0 → x = −1
x + 3 = 0 → x = −3
x = -3, -1
How to solve 3x^2+12x+9
To solve 3x^2+12x+9, we can try factoring, use the quadratic formula, or complete the square. The solution is x = -3, -1.
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+12x+9?
The answer is x = -3, -1.
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+12x+9 confirms both sides are equal.