If the roots of the equation x² + 5x + k = 0 are 1 and 4, find k. (2020)

If the roots of the equation x² + 5x + k = 0 are 1 and 4, find k. (2020)

Step 1: Identify the given quadratic equation, which is x² + 5x + k = 0.
Step 2: Recognize that the roots of the equation are given as 1 and 4.
Step 3: Use the product of the roots formula, which states that the product of the roots (1 * 4) equals k.
Step 4: Calculate the product: 1 * 4 = 4, so k = 4.
Step 5: Use the sum of the roots formula, which states that the sum of the roots (1 + 4) should equal -b/a, where b is the coefficient of x.
Step 6: Calculate the sum: 1 + 4 = 5, which matches the coefficient of x in the equation (5).
Step 7: Since both the product and sum conditions are satisfied, we confirm that k = 4.

No concepts available.