Example 3: Find the quadratic equation if we know that the roots are 2 and 3.
It is easy to find the solutions of the x from the square equation by the following steps.
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(1) |
Now we can add and multiply the solutions to get the solutions as a function of the coefficients of the square equation.
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(2)
(3) |
Substitute given solutions into equations (2) and (3).
b = −(x1 + x2)a = −(2 + 3)a = −5a
c = x1x2a = 2 ‧ 3a = 6a
If we chose a to be equal to 1 than the quadratic equation will be: x2 − 5x + 6 = 0
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