The quadratic equation x^2 + 6x + k = 0 has equal roots. What is the value of k?
Practice Questions
Q1
The quadratic equation x^2 + 6x + k = 0 has equal roots. What is the value of k? (2020)
9
12
16
36
Questions & Step-by-Step Solutions
The quadratic equation x^2 + 6x + k = 0 has equal roots. What is the value of k? (2020)
Step 1: Identify the quadratic equation, which is x^2 + 6x + k = 0.
Step 2: Recognize that for a quadratic equation to have equal roots, the discriminant must be zero. The discriminant is given by the formula b^2 - 4ac.
Step 3: In our equation, a = 1, b = 6, and c = k.
Step 4: Substitute the values of a, b, and c into the discriminant formula: 6^2 - 4(1)(k) = 0.
Step 5: Calculate 6^2, which is 36. So, we have 36 - 4k = 0.
Step 6: Rearrange the equation to solve for k: 36 = 4k.
Step 7: Divide both sides by 4 to find k: k = 36 / 4.
Step 8: Calculate 36 / 4, which equals 9. Therefore, k = 9.
