Multiple choice

The values of k for which the given quadratic equation has real and distinct roots $x^2$ - kx + 9 = 0 is $k < -6$ $or$ $ k > 6$.

  1. True

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

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

AI explanation

For a quadratic equation to have real and distinct roots, its discriminant must be strictly greater than zero. For the equation x squared minus k x plus 9 equals 0, the discriminant is k squared minus 4 times 1 times 9. Setting this greater than zero gives k squared minus 36 is greater than 0, which means k squared is greater than 36. Therefore, k must be less than negative 6 or greater than 6, making the statement true.

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