If the quadratic equation x^2 + 2x + k = 0 has one root equal to -1, what is the

₹0.0

Question: If the quadratic equation x^2 + 2x + k = 0 has one root equal to -1, what is the value of k? (2022)

Options:

Correct Answer: 1

Exam Year: 2022

Solution:

Substituting x = -1 into the equation gives (-1)^2 + 2(-1) + k = 0, leading to 1 - 2 + k = 0, thus k = 1.

If the quadratic equation x^2 + 2x + k = 0 has one root equal to -1, what is the value of k? (2022)

If the quadratic equation x^2 + 2x + k = 0 has one root equal to -1, what is the value of k? (2022)

Step 1: Start with the quadratic equation x^2 + 2x + k = 0.
Step 2: We know one root of the equation is -1. This means we can substitute x with -1 in the equation.
Step 3: Substitute -1 into the equation: (-1)^2 + 2(-1) + k = 0.
Step 4: Calculate (-1)^2, which is 1.
Step 5: Calculate 2(-1), which is -2.
Step 6: Now, rewrite the equation with these values: 1 - 2 + k = 0.
Step 7: Simplify the left side: 1 - 2 equals -1, so we have -1 + k = 0.
Step 8: To find k, add 1 to both sides of the equation: k = 1.

Quadratic Equations – Understanding the structure of quadratic equations and how to find roots by substituting values.
Substitution Method – Using substitution to solve for unknowns in equations.