Multiple choice

For what value of (k), will the roots of the equation (kx^2 - 5x + 6 = 0) be in the ratio of 2 : 3?

  1. 0

  2. 1

  3. -1

  4. 2
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For roots in ratio 2:3, let roots be 2a and 3a. Using Vieta's formulas: Sum = 5/k = 5a, so a = 1/k. Product = 6/k = 6a^2 = 6(1/k^2). Therefore 6/k = 6/k^2, which gives k = 1. Verification: with k=1, equation is x^2 - 5x + 6 = 0, giving roots 2 and 3, which are in ratio 2:3. Option A (k=0) is invalid - equation would be -5x + 6 = 0 with only one root. Option C gives roots 2 and 1.5 (ratio 4:3). Option D gives roots 1.5 and 2 (ratio 3:4).

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