If the roots of the quadratic equation x^2 - 6x + k = 0 are in the ratio 1:2, what is the value of k?
Answer and explanation
Correct answer: B. 8
- Step 1: Let the roots be r and 2r.
- Step 2: Sum of roots: r + 2r = 3r = -(-6) / 1 = 6 => r = 2.
- Step 3: The roots are 2 and 4.
- Step 4: Product of roots: k = 2 * 4 = 8.
Answer
8.
Why not the others: '9' assumes equal roots (r = 3, k = 3*3); '4' assumes r = 1; '12' multiplies sum of roots by 2.
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