16 (a) Use the iteration formula $x_{n} = \sqrt{10 - 2x_{n-1}}$ to find the values of $x_{1}$, $x_{2}$, and $x_{3}$ - Edexcel - GCSE Maths - Question 16 - 2021 - Paper 2

Using the obtained values, we know:

• $x_{1} \approx 2.45$, $x_{2} \approx 2.26$, $x_{3} \approx 2.34$. We can form the quadratic equation from these values. From the quadratic form $x^{2} + ax + b = 0$:

By substituting $x_1$ and $x_2$ into the equation: $a = - (x_{1} + x_{2}) \approx - (2.45 + 2.26) = - 4.71 \approx -5$ $b = x_{1} \times x_{2} \approx 2.45 \times 2.26 \approx 5.54 \approx 6$

Hence,

• $a \approx -5$
• $b \approx 6$