Multiple choice

The value of k for which the given quadratic has real and distinct roots $kx^2$ + 6x + 1 = 0 is k < 9

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For real and distinct roots, the discriminant b^2 - 4ac > 0. Here, a=k, b=6, c=1. So 6^2 - 4(k)(1) > 0, which means 36 - 4k > 0, or 36 > 4k, so k < 9.

AI explanation

For real and distinct roots, the discriminant b^2 - 4ac must be greater than zero, requiring 6^2 - 4(k)(1) > 0. This simplifies to 36 - 4k > 0, meaning 4k < 36 and k < 9. The condition also requires that k not be zero to remain a quadratic, but the primary inequality k < 9 is the governing condition for the statement; the statement is true.

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