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If f(x)=3x2−5x+2f(x) = 3x^2 - 5x + 2, what is f′(x)f'(x)?
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Solve 2x2−3x−2=02x^2 - 3x - 2 = 0 for xx. (3 marks)

Worked solution

  1. 1.Factorise: 2x2−3x−2=(2x+1)(x−2)2x^2-3x-2=(2x+1)(x-2).
  2. 2.Set each factor to zero: 2x+1=02x+1=0 or x−2=0x-2=0.
  3. 3.Solve each: x=−12x=-\dfrac{1}{2} or x=2x=2.

A student's answer

(2x+1)(x−2)=0(2x+1)(x-2)=0so x=2x=2

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