Solve 2x^2-3x-2 = 0
Solve ax² + bx + c = 0 using the quadratic formula with discriminant analysis.
2x2-3x-2=0
Solve by factoring the quadratic and applying the zero product property:
When the leading coefficient is 2 (not 1), multiply a × c to find the product, then find a pair that adds to b:
a × c = 2 × -2 = -4
Find two numbers that multiply to -4 and add to -3:
-4 × 1 = -4, -4 + 1 = -3
Rewrite −3x as −4x +x:
2x2 − 4x + x − 2
Group and factor each pair:
(2x2 − 4x) + (x − 2)
= (x - 2)(2x + 1)
If a product equals zero, at least one of the factors must be zero. Set each factor equal to zero and solve:
2x + 1 = 0
2x = −1
x = −1 / 2 = −12
x − 2 = 0 → x = 2
x = -12, 2
How to solve 2x^2-3x-2 = 0
To solve 2x^2-3x-2 = 0, we can try factoring, use the quadratic formula, or complete the square. The solution is x = -1/2, 2.
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 2x^2-3x-2 = 0?
The answer is x = -1/2, 2.
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 2x^2-3x-2 = 0 confirms both sides are equal.