Solve: x² + 9x + 14 > 0
Using quadratic inequality
To solve the quadratic inequality x² + 9x + 14 > 0, we can use the following steps:
Step 1: Factorize the quadratic expression.
The given expression can be factored as (x + 2)(x + 7) > 0.
Step 2: Determine the sign of each factor.
The sign of (x + 2) is positive for x > -2 and negative for x < -2.
The sign of (x + 7) is positive for x > -7 and negative for x < -7.
Step 3: Determine the sign of the product.
To find the sign of the product (x + 2)(x + 7), we can use a sign table.
Sign Table:
| x < -7 | -7 < x < -2 | x > -2
------------------------------------------------
x + 2 | - | + | +
x + 7 | - | + | +
Step 4: Determine the solution set.
From the sign table, we can see that the product (x + 2)(x + 7) is positive when x < -7 or x > -2.
Therefore, the solution to the inequality x² + 9x + 14 > 0 is x < -7 or x > -2.
In interval notation, the solution is (-∞, -7) U (-2, ∞).
Post a Comment
Post a Comment