Algebra 5

4 marks · Hard

Solve the equation by factorising, and write down all possible values of as exact values.

Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.

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x = \frac{5}{2},\; x = -1

Also accept: x = -1,\; x = \frac{5}{2}

Common mistakes: Subtracting incorrectly; e.g. 2x^2 - 3x + 5 = 0; Errors factorising 2x^2 - 3x - 5

Show mark scheme and worked solution

Marking points

M1 · 1 mark · Rearranges equation to

M1b · 1 mark · Attempts correct factorisation of the quadratic expression

A1 · 1 mark · Obtains correct factors: (2x + 5)(x - 1) or equivalent

A1b · 1 mark · Finds both values: and , or equivalent accurate exact values

Worked solution

Start with the equation:

Rearrange to one side:

Factorise:

Set each bracket to zero:

So, the solutions are and .