Multiple choice

Find the incomplete quadratic equation in $x$, whose solution is $\pm\dfrac{5}{2}$.

  1. $\dfrac{25}{16}x^{2} + 4x = 0$
  2. $\dfrac{16}{25}x^{2} - 4 = 0$
  3. $\dfrac{15}{25}x^{2} - 4 = 0$
  4. $\dfrac{4}{2}x^{2} = 0$
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B Correct answer
Explanation

If roots are +/- 5/2, the equation is (x - 5/2)(x + 5/2) = 0, which is x^2 - 25/4 = 0. Multiplying by 16/25 gives (16/25)x^2 - 4 = 0.

AI explanation

An incomplete quadratic equation with no linear (x) term and solutions of x = 5/2 and x = -5/2 takes the form x^2 - (25/4) = 0. Multiplying the entire equation by 16/25 yields (16/25)x^2 - 4 = 0.

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