GCSE OCR Maths Solving quadratic equations: Solve by factorisation. $$2x^2

Solve by factorisation - OCR - GCSE Maths - Question 18 - 2017 - Paper 1

Question 18

Solve by factorisation. $$2x^2 + 5x - 12 = 0$$ (a) $x = \ldots$ or $x = \ldots$ (b) Solve this equation. Give each value correct to 2 decimal places. $$3x^2 + ... show full transcript

Worked Solution & Example Answer:Solve by factorisation - OCR - GCSE Maths - Question 18 - 2017 - Paper 1

Step 1

Solve by factorisation.

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Answer

To solve the equation $2x^2 + 5x - 12 = 0$ by factorisation, we need to express it in the form of two binomial factors.

Finding Factors: We look for two numbers that multiply to give $2 \times -12 = -24$ and add up to $5$ . The numbers $6$ and $-4$ satisfy this condition.
Rewriting the Equation: We can rewrite the middle term:

$2x^2 + 6x - 4x - 12 = 0$
Grouping: Next, group the terms:

$(2x^2 + 6x) + (-4x - 12) = 0$

Factor out the common terms:

$2x(x + 3) - 4(x + 3) = 0$

Now, factor by grouping:

$(2x - 4)(x + 3) = 0$
Setting Each Factor to Zero: We set each factor to zero:

$2x - 4 = 0$ or $x + 3 = 0$ .
Solving for x:
- From $2x - 4 = 0$ , we get $x = 2$ .
- From $x + 3 = 0$ , we find $x = -3$ .

Thus, the solutions are:

$x = 2$ or $x = -3$ .

Step 2

Solve this equation. Give each value correct to 2 decimal places.

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Answer

To solve $3x^2 + 2x - 3 = 0$ , we will use the quadratic formula:

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ , where $a = 3$ , $b = 2$ , and $c = -3$ .

Calculating the Discriminant:

$b^2 - 4ac = 2^2 - 4 \times 3 \times -3 = 4 + 36 = 40$
Using the Quadratic Formula:

$x = \frac{-2 \pm \sqrt{40}}{2 \times 3}$
Simplifying:

$x = \frac{-2 \pm 2\sqrt{10}}{6} = \frac{-1 \pm \sqrt{10}}{3}$
Calculating the Roots:
- For $x = \frac{-1 + \sqrt{10}}{3}$ :
  
  Evaluating $\sqrt{10} \approx 3.162$ gives:
  
  $x \approx \frac{-1 + 3.162}{3} \approx \frac{2.162}{3} \approx 0.72$
- For $x = \frac{-1 - \sqrt{10}}{3}$ :
  
  Evaluating gives: $x \approx \frac{-1 - 3.162}{3} \approx \frac{-4.162}{3} \approx -1.39$

Thus, the solutions are:

$x \approx 0.72$ or $x \approx -1.39$ .

Solve by factorisation - OCR - GCSE Maths - Question 18 - 2017 - Paper 1

Worked Solution & Example Answer:Solve by factorisation - OCR - GCSE Maths - Question 18 - 2017 - Paper 1

Solve by factorisation.

Solve this equation. Give each value correct to 2 decimal places.

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