Multiple choice

How many roots can be common between two Quadratic Equations?

  1. Only $1$
  2. More than $2$
  3. Not more than $2$

  4. No roots can be common
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C Correct answer
Explanation

A quadratic equation has at most 2 roots. Two distinct quadratic equations can share at most 2 roots (if they are identical) or 1 root (if they are not). Thus, the maximum number of common roots is 2.

AI explanation

A quadratic equation is a polynomial equation of the second degree, so it has exactly two roots. If two distinct quadratic equations share both of their roots, they are fundamentally the same equation. Therefore, the maximum number of common roots two different quadratic equations can have is not more than 2.

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