Multiple choice

The common root of the equations $x^{2}-7x+10=0 $ and $x^{2}-10x+16=0$ is:

  1. -2

  2. 2

  3. 3

  4. 5
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Factorize the equations: x^2 - 7x + 10 = (x-2)(x-5) = 0, so roots are 2, 5. x^2 - 10x + 16 = (x-2)(x-8) = 0, so roots are 2, 8. The common root is 2.

AI explanation

To find the common root, we can solve both quadratic equations. Factoring the first equation gives (x - 5)(x - 2) = 0, yielding roots 5 and 2. Factoring the second equation gives (x - 8)(x - 2) = 0, yielding roots 8 and 2. The root that appears in the solution sets of both equations is 2.

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