Multiple choice

Find the roots of the following quadratic equation by using the quadratic formula $4{x^2} + 3x + 5 = 0$

  1. $\dfrac{{3 + \sqrt {71i} }}{8}$
  2. $\dfrac{{3 + \sqrt {89i} }}{8}$
  3. $\dfrac{{ - 3 \pm \sqrt {71i} }}{8}$
  4. $\dfrac{{ - 3 \pm \sqrt {89i} }}{8}$
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C Correct answer
AI explanation

Using the quadratic formula to solve 4x^2 + 3x + 5 = 0, we have x = (-b ± sqrt(b^2 - 4ac)) / 2a. Substituting a = 4, b = 3, and c = 5 gives x = (-3 ± sqrt(3^2 - 4(4)(5))) / 2(4). This simplifies to x = (-3 ± sqrt(9 - 80)) / 8, which further simplifies to (-3 ± sqrt(-71)) / 8. Because sqrt(-71) is the imaginary number sqrt(71i), the roots are (-3 ± sqrt(71i)) / 8.

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