Multiple choice

The set of values of k for which the given quadratic equation has real roots $2x^2$ + kx + 4 = 0 is k $\geq \, 4\sqrt{2}$ and $k\le-4\sqrt{2}$

  1. True

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

For real roots, D = k^2 - 4(2)(4) >= 0. k^2 - 32 >= 0. k^2 >= 32. k >= sqrt(32) or k <= -sqrt(32). sqrt(32) = 4*sqrt(2).

AI explanation

For a quadratic equation to have real roots, the discriminant must be greater than or equal to zero, meaning b^2 - 4ac >= 0. Substituting the coefficients gives k^2 - 4(2)(4) >= 0, which simplifies to k^2 >= 32. Taking the square root of both sides shows that k must be greater than or equal to 4*sqrt(2) or less than or equal to -4*sqrt(2); the statement is true.

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