Let $f(x) = x^2 + bx + c$ and $g(x) = x^2 + dx + e$ - AQA - A-Level Maths Mechanics - Question 4 - 2019 - Paper 2
Question 4
Let $f(x) = x^2 + bx + c$ and $g(x) = x^2 + dx + e$. Given that both $f(x)$ and $g(x)$ have a common factor $(x + 2)$, it follows from the factor theorem that:
1. $... show full transcript
Worked Solution & Example Answer:Let $f(x) = x^2 + bx + c$ and $g(x) = x^2 + dx + e$ - AQA - A-Level Maths Mechanics - Question 4 - 2019 - Paper 2
Step 1
Show that $2(d - b) = e - c$
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Answer
Use the factor theorem to substitute x=−2 into the first expression:
4−2b+c=0⇒c=2b−4
Repeat this for the second expression:
4−2d+e=0⇒e=2d−4
Set up the equation you are trying to prove:
2(d−b)=(2d−4)−(2b−4)
Simplifying the right-hand side gives:
2d−4−2b+4=2d−2b
Thus, we see that both sides are equal:
2(d−b)=2d−2b
