Multiple choice

Form the quadratic equation whose roots are: $\displaystyle \frac{3}{4}$ and $\displaystyle \frac{-3}{4}$

  1. $16x^{2}\, +\, 9\, =\, 0$
  2. $16x^{2}\, -\, 9\, =\, 0$
  3. $4x^{2}\, -\, 9\, =\, 0$
  4. $4x^{2}\, +\, 9\, =\, 0$
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B Correct answer
Explanation

If roots are 3/4 and -3/4, the equation is (x - 3/4)(x + 3/4) = 0, which is x^2 - 9/16 = 0. Multiplying by 16 gives 16x^2 - 9 = 0.

AI explanation

The sum of the roots is (3/4) + (-3/4) = 0 and the product of the roots is (3/4) * (-3/4) = -9/16. The required quadratic equation is x^2 - (sum)x + (product) = 0, resulting in x^2 - 0x - 9/16 = 0. Multiplying the equation by 16 to clear the denominator gives 16x^2 - 9 = 0.

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