Multiple choice

If the difference between the roots of the equation Ax2 - Bx + C = 0 is 4, then which of the following is TRUE?

  1. B2 - 16A2 = 4AC + 4B2

  2. B2 - 10A2 = 4AC + 6A2

  3. B2 - 8A2 = 4AC + 10A2

  4. B2 - 16A2 = 4AC + 8B2
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For Ax^2 - Bx + C = 0, roots are (B +/- sqrt(B^2 - 4AC)) / 2A. The difference is sqrt(B^2 - 4AC) / A = 4. Squaring both sides gives (B^2 - 4AC) / A^2 = 16, so B^2 - 4AC = 16A^2. Rearranging gives B^2 - 16A^2 = 4AC. Option B is B^2 - 10A^2 = 4AC + 6A^2, which simplifies to B^2 - 16A^2 = 4AC. Both are mathematically equivalent.

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