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Mathematics · Grades 9–11

Roots from factors

Set each factor equal to zero and check the original equation.

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The key idea

Set each factor equal to zero and check the original equation.

uv = 0 → u = 0 or v = 0

Worked examples

Find the smaller root of (x − 24)(x − 26) = 0.

x = 24 or x = 26; 24 < 26

24

Find the smaller root of (x − 19)(x − 31) = 0.

x = 19 or x = 31; 19 < 31

19

Try it yourself

  1. Find the smaller root of (x − 4)(x − 9) = 0.

  2. Find the smaller root of (x − 5)(x − 6) = 0.

Check your understanding

Answers and marking notes
  1. 4

    x = 4 or x = 9; 4 < 9

  2. 5

    x = 5 or x = 6; 5 < 6

Further reading and review references

These are reference links, not copied exercises, institutional endorsement or proof of independent review.

Learning preview · teacher review required. Grade bands are approximate, not official curriculum alignment.