Multiple choice

The set of values of k for which the given quadratic equation has real roots $4x^2$ - 3kx + 1 = 0 is k $\leq \, -\dfrac{4}{3}$ or k $\geq \, \dfrac{4}{3}$

  1. True

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

For real roots, the discriminant D = (-3k)^2 - 4(4)(1) >= 0. So 9k^2 - 16 >= 0, which means k^2 >= 16/9. This implies k >= 4/3 or k <= -4/3.

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 (-3k)^2 - 4(4)(1) >= 0, which simplifies to 9k^2 - 16 >= 0. Factoring this as a difference of squares yields (3k - 4)(3k + 4) >= 0, which means k <= -4/3 or k >= 4/3; the statement is true.

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