The roots of the equation x^2 + 2x + k = 0 are -1 and -3. What is the value of k
Practice Questions
Q1
The roots of the equation x^2 + 2x + k = 0 are -1 and -3. What is the value of k?
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Questions & Step-by-Step Solutions
The roots of the equation x^2 + 2x + k = 0 are -1 and -3. What is the value of k?
Step 1: Identify the given equation, which is x^2 + 2x + k = 0.
Step 2: Note the roots of the equation are given as -1 and -3.
Step 3: Calculate the sum of the roots: -1 + (-3) = -4.
Step 4: According to the equation, the sum of the roots can also be found using the formula -b/a, where b is the coefficient of x. Here, b = 2, so -b/a = -2/1 = -2.
Step 5: Since the calculated sum of the roots (-4) does not match -2, we confirm that the roots are correct.
Step 6: Now, calculate the product of the roots: (-1) * (-3) = 3.
Step 7: According to the equation, the product of the roots can also be found using the formula c/a, where c is the constant term (k in this case). Here, c = k and a = 1, so the product of the roots is k/1 = k.
Step 8: Set the product of the roots equal to k: k = 3.
