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Solve by factorisation - OCR - GCSE Maths - Question 16 - 2018 - Paper 1

Question 16

Solve by factorisation. 3x² + 11x - 20 = 0 x = .................... or x = ....................

Worked Solution & Example Answer:Solve by factorisation - OCR - GCSE Maths - Question 16 - 2018 - Paper 1

Step 1

Factor the quadratic equation

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Answer

The equation to solve is:

$3x^2 + 11x - 20 = 0$

To factor this equation, we look for two numbers that multiply to give the product of the coefficient of $x^2$ (which is 3) and the constant term (which is -20), hence $3 \times -20 = -60$ , and that also add to give the coefficient of $x$ , which is 11. The numbers 15 and -4 meet these criteria since:

$15 \times (-4) = -60$ $15 + (-4) = 11$

Thus, we can rewrite the middle term as:

$3x^2 + 15x - 4x - 20 = 0$

Next, group the terms:

$(3x^2 + 15x) + (-4x - 20) = 0$

Step 2

Complete the factorisation

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Answer

Factoring out common terms from each group:

$3x(x + 5) - 4(x + 5) = 0$

Now factor out the common binomial $(x + 5)$ :

$(3x - 4)(x + 5) = 0$

Step 3

Solve for x

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Answer

Now, set each factor to zero:

$3x - 4 = 0$
- Solving for $x$ gives: $3x = 4 \Rightarrow x = \frac{4}{3}$
$x + 5 = 0$
- Solving for $x$ gives: $x = -5$

Thus, the solutions are:

$x = \frac{4}{3} \text{ or } x = -5$

Solve by factorisation - OCR - GCSE Maths - Question 16 - 2018 - Paper 1

Worked Solution & Example Answer:Solve by factorisation - OCR - GCSE Maths - Question 16 - 2018 - Paper 1

Factor the quadratic equation

Complete the factorisation

Solve for x

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