23 (a) Factorise $x^2 + 10x + 24$.
(b) Write down the solutions to $x^2 + 10x + 24 = 0$.
Worked Solution & Example Answer:23 (a) Factorise $x^2 + 10x + 24$ - OCR - GCSE Maths - Question 23 - 2023 - Paper 2
Step 1
Factorise $x^2 + 10x + 24$
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Answer
To factorise the quadratic expression x2+10x+24, we need to find two numbers that multiply to 24 (the constant term) and add up to 10 (the coefficient of the linear term). The numbers 6 and 4 fulfill these conditions since:
6×4=24
6+4=10
Thus, we can express the quadratic as:
x2+10x+24=(x+6)(x+4)
Step 2
Write down the solutions to $x^2 + 10x + 24 = 0$
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Answer
To find the solutions of the equation x2+10x+24=0, we can use the factored form we found earlier:
(x+6)(x+4)=0
Setting each factor to zero gives us:
