Worksheet: Solving Quadratic Equations Iteratively

In this worksheet, we will practice solving quadratic equations using an iterative process.

Q1:

The equation of the following graph is 𝑦=𝑥8𝑥+8. Use the iterative formula 𝑥=88𝑥, starting with 𝑥=7, to find the largest root of the equation 𝑥8𝑥+8=0 to 4 decimal places.

Q2:

The equation of the following graph is 𝑦=𝑥+3𝑥9. Use the iterative formula 𝑥=9𝑥3, starting with 𝑥=5, to find the negative root of the equation 𝑥+3𝑥9=0 to 4 decimal places.

Q3:

The equation of the following graph is 𝑦=𝑥2𝑥+7. Use the iterative formula 𝑥=7𝑥+2, starting with 𝑥=2, to find the positive root of the equation 𝑥2𝑥+7=0 to 4 decimal places.

Q4:

The equation of the following graph is 𝑦=𝑥+5𝑥13.

Use the iterative formula 𝑥=135+𝑥, starting with 𝑥=2, to find the positive root of the equation 𝑥+5𝑥13=0 to 4 decimal places.

Use the iterative formula 𝑥=13𝑥5, starting with 𝑥=7, to find the negative root of the equation 𝑥+5𝑥13=0 to 4 decimal places.

Q5:

The equation of the following graph is 𝑦=𝑥+8𝑥14. Use the iterative formula 𝑥=14𝑥8, starting with 𝑥=3, to find the smallest root of the equation 𝑥+8𝑥14=0 to 4 decimal places.

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