Multiple choice

If (x - 2)2 = a, for what value of 'a' will the equation have equal roots?

  1. 0

  2. 2

  3. 4

  4. 8
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A Correct answer
Explanation

The equation (x - 2)^2 = a is equivalent to x^2 - 4x + 4 - a = 0. For a quadratic equation to have equal roots, the discriminant must be zero. Discriminant = (-4)^2 - 4(1)(4 - a) = 16 - 16 + 4a = 4a. Setting 4a = 0 gives a = 0.

AI explanation

The given equation is (x - 2)^2 = a, which can be expanded to x^2 - 4x + 4 - a = 0. For a quadratic equation to have equal roots, its discriminant must be equal to zero. Setting the discriminant b^2 - 4ac to zero gives (-4)^2 - 4(1)(4 - a) = 0, which simplifies to 16 - 16 + 4a = 0. Solving this yields a = 0.

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