Multiple choice

Form the quadratic equation if its roots are: $\displaystyle\,\frac{1}{2}$ and $\cfrac{-1}{2}$

  1. $4x^2\,-\,1\,=\,0$
  2. $4x^2\,-\,4\,=\,0$
  3. $4x^2\,+\,1\,=\,0$
  4. $4x^2\,-\,3\,=\,0$
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A Correct answer
Explanation

If roots are 1/2 and -1/2, the equation is (x - 1/2)(x + 1/2) = 0, which is x^2 - 1/4 = 0. Multiplying by 4 gives 4x^2 - 1 = 0.

AI explanation

Using the sum and product of roots formula, the required quadratic equation is x^2 - (sum of roots)x + (product of roots) = 0. The sum of the roots 1/2 and -1/2 is 0, and their product is -1/4. Substituting these values gives x^2 - 0x - 1/4 = 0, which simplifies to 4x^2 - 1 = 0.

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