X^2+3x+2
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x^2 + 3x + 2 =
(x+1)(x+2),
post
To solve the quadratic equation X^2 + 3X + 2, we can use two common methods: factoring and using the quadratic formula.
Method 1: Factoring
1. Write the equation in the form of (X + a)(X + b), where 'a' and 'b' are the factors of the constant term (2) that add up to the coefficient of the linear term (3).
(X + 1)(X + 2) = 0
2. Set each factor equal to zero and solve for X:
X + 1 = 0 or X + 2 = 0
X = -1 or X = -2
Therefore, the solutions to the equation X^2 + 3X + 2 = 0 are X = -1 and X = -2.
Method 2: Quadratic Formula
The quadratic formula helps us find the roots of any quadratic equation ax^2 + bx + c = 0, where 'a', 'b', and 'c' are constants.
1. Identify the values of 'a', 'b', and 'c' from the equation X^2 + 3X + 2 = 0:
a = 1, b = 3, c = 2
2. Plug these values into the quadratic formula:
X = (-b ± √(b^2 - 4ac))/(2a)
X = (-(3) ± √((3)^2 - 4(1)(2)))/(2(1))
3. Simplify the equation inside the square root:
X = (-3 ± √(9 - 8))/(2)
X = (-3 ± √(1))/(2)
X = (-3 ± 1)/(2)
4. Solve for both possible values:
X = (-3 + 1)/2 or X = (-3 - 1)/2
X = -2/2 or X = -4/2
X = -1 or X = -2
Again, the solutions to the equation X^2 + 3X + 2 = 0 are X = -1 and X = -2.