Multiple choice

If the equation $9x^2-4kx + 4 = 0$ has two equal roots, k is equal to

  1. $\pm 1$
  2. $2$
  3. $\pm 3$
  4. $\pm 4$
  5. $5$
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C Correct answer
Explanation

For a quadratic equation ax^2 + bx + c = 0 to have equal roots, the discriminant D = b^2 - 4ac must be 0. Here, a=9, b=-4k, c=4. So, (-4k)^2 - 4(9)(4) = 0, which simplifies to 16k^2 - 144 = 0. Thus, k^2 = 9, meaning k = +/- 3.

AI explanation

For a quadratic equation to have two equal real roots, its discriminant must equal zero, so b^2 - 4ac = 0. Substituting the values gives (-4k)^2 - 4(9)(4) = 0. Simplifying this results in 16k^2 - 144 = 0, which means k^2 = 9. Taking the square root of both sides gives k = 3 or k = -3.

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