f one of the two roots of x²- 4x - k = 0 is twice the other roots, then find the value of k.
Question
f one of the two roots of x²- 4x - k = 0 is twice the other roots, then find the value of k.
Solution
Let's solve this step by step:
Step 1: Let's assume the roots of the equation are a and 2a.
Step 2: According to Vieta's formulas, the sum of the roots is equal to -b/a, and the product of the roots is equal to c/a. In this case, a is 1, b is -4, and c is -k.
Step 3: So, a + 2a = -(-4) = 4, which gives 3a = 4, so a = 4/3.
Step 4: The product of the roots is a * 2a = 2a² = 2*(4/3)² = 2*(16/9) = 32/9.
Step 5: Therefore, -k = 32/9, so k = -32/9.
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