Multiple choice

For what value of k, will the roots of the equation kx2-5x+6=0 be in the ratio of 2 : 3? समीकरण kx2-5x+6=0 में k के किस मान के लिए उसके मूल 2 : 3 अनुपात में होंगे?

  1. 0

  2. 1

  3. -1

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

For the equation kx² - 5x + 6 = 0 to have roots in ratio 2:3, let roots be 2α and 3α. By Vieta's formulas: Sum = 2α + 3α = 5α = 5/k, and Product = 2α × 3α = 6α² = 6/k. From sum: α = 1/k. Substituting in product: 6(1/k)² = 6/k, which gives k = 1. This satisfies the condition.

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