Given values a1, b1 and c1 of first Quadratic equations and values a2, b2 and c2 of second Quadratic equations , the task is to find whether both quadratic equations have common roots or not.
Input: a1 = 1, b1 = -5, c1 = 6, a2 = 2, b2 = -10, c2 = 12
Roots of both quadratic equations are (2, 3)
Input: a1 = 1, b1 = -5, c1 = 6, a2 = 1, b2 = -9, c2 = 20
Roots of first quadratic equations are (2, 3), and Roots of second quadratic equations are (4, 5)
Therefore, both quadratic equations have differnt roots.
Let the two quadratic equations are and
- Let us assume the given condition to be true, i.e. both the equations have common roots, say and
- As we know that
where a, b, c represents the quadratic equation
For 1st quadratic equation:
Similarly, for 2nd quadratic equation:
- Now since both the roots are common,
Therfore, from above equations
- Combining the above equations:
which is the required condition for both roots to be common of the two quadratic equations.
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