# One of the roots of the equation x * x-13x + q = 0 is 12.5. find another root and coefficient q

July 28, 2021 | education

| Let’s write the quadratic equation:

x ^ 2 – 13 * x + q = 0; is the reduced quadratic equation,

by Vietta’s Theorem, we write:

x1 * x2 = q;

x1 + x2 = 13;

If x1 = 12.5, then from the equation x1 + x2 = 13;

Find x2: 12.5 + x2 = 13;

hence x2 = 0.5.

Find q from the equation x1 * x2 = q: 12.5 * 0.5 = 6.25.

Answer: x2 = 0.5; q = 6.25.

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