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NECO 2023 · Paper 1 · Q20

Find a quadratic equation whose roots are 2 and −13-\frac13.

Worked solution (try it first)
  1. Roots 2 and −13-\frac13 give the factors (x−2)(x - 2) and (x+13)\left(x + \frac13\right).
  2. Multiply the second factor by 3 to clear the fraction: (x−2)(3x+1)=0(x - 2)(3x + 1) = 0.
  3. Expand: 3x2+x−6x−2=3x2−5x−23x^2 + x - 6x - 2 = 3x^2 - 5x - 2.
  4. So the equation is 3x2−5x−2=03x^2 - 5x - 2 = 0, option B.

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