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WAEC 2022 · Paper 1 · Q6

The functions f:x→2x2+3x−7f: x \to 2x^2 + 3x - 7 and g:x→5x2+7x−6g: x \to 5x^2 + 7x - 6 are defined on the set of real numbers, RR. Find the values of xx for which 3f(x)=g(x)3f(x) = g(x).

Worked solution (try it first)
  1. Multiply ff by 3: 3f(x)=6x2+9x−213f(x) = 6x^2 + 9x - 21.
  2. Set it equal to g(x)g(x) and bring everything to one side: 6x2+9x−21−5x2−7x+6=06x^2 + 9x - 21 - 5x^2 - 7x + 6 = 0, so x2+2x−15=0x^2 + 2x - 15 = 0.
  3. Factorise: (x+5)(x−3)=0(x + 5)(x - 3) = 0.
  4. So x=−5x = -5 or x=3x = 3, option C.

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