Multiple choice

If the roots of the equations 6x2 – 7x + k = 0 are rational. The k is equal to

  1. –1

  2. –1, –2

  3. –2

  4. 1, 2
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For roots to be rational, the discriminant D = b^2 - 4ac must be a perfect square. D = (-7)^2 - 4(6)(k) = 49 - 24k. For 49 - 24k to be a perfect square, testing k=1 gives 25 (square), testing k=2 gives 1 (square).

AI explanation

For the quadratic equation to have rational roots, its discriminant must be a perfect square. The discriminant is (-7)^2 - 4(6)(k) = 49 - 24k. Testing the provided pairs for k, if k = 1, the discriminant is 25; and if k = 2, the discriminant is 1, both of which are perfect squares.

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