Multiple choice

The set of values of k for which the given quadratic equation has real roots $x^2$ - kx + 9 = 0 is k $\leq$ -6 or k $\geq$ 6

  1. True

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

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

AI explanation

For a quadratic equation to have real roots, its discriminant must be greater than or equal to 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 or equal to zero gives k squared minus 36 is greater than or equal to 0, meaning k squared is greater than or equal to 36. Therefore, k must be less than or equal to negative 6 or greater than or equal to 6, making the statement true.

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