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The difference between the roots of a quadratic is 4i. The sum of the roots is 12. Write the equation.

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The equation whose difference between the roots of a quadratic is 4i and The sum of the roots is 12 is; x² -12x + 40 = 0

According to the question;

  • The difference between the roots of a quadratic is 4i. The sum of the roots is 12.

In essence,

  • f - g = 4i

  • f + g = 12

By solving simultaneously;

  • f = 6 + 2i. and. g = 6 - 2i

The equation can therefore be written as follows;

  • (x - 6 -2i) (x -6 +2i) = 0

The equation is therefore;

x² -12x + 40 = 0

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