Worksheet: Solving Cubic Equations Iteratively

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

Q1:

The equation of the following graph is 𝑦=𝑥+𝑥5𝑥+1. Use the iterative formula 𝑥=𝑥+5𝑥1, starting with 𝑥=3, to find the negative root of the equation 𝑥+𝑥5𝑥+1=0 to 4 decimal places.

Q2:

The equation of the following graph is 𝑦=𝑥𝑥6𝑥+2. Use the iterative formula 𝑥=𝑥+6𝑥2, starting with 𝑥=3, to find the largest root of the equation 𝑥𝑥6𝑥+2=0 to 4 decimal places.

Q3:

The equation of the following graph is 𝑦=𝑥+𝑥+5𝑥+2. Use the iterative formula 𝑥=𝑥+5𝑥+2, starting with 𝑥=3, to find the positive root of the equation 𝑥+𝑥+5𝑥+2=0 to 4 decimal places.

Q4:

The equation of the following graph is 𝑦=𝑥+2𝑥8𝑥+3. Use the iterative formula 𝑥=2𝑥+8𝑥3, starting with 𝑥=4, to find the smallest root of the equation 𝑥+2𝑥8𝑥+3=0 to 3 decimal places.

Q5:

The equation of the following graph is 𝑦=𝑥𝑥5. An approximate solution to the equation 𝑥𝑥=5 is found using the iterative formula 𝑥=𝑥+5, starting with 𝑥=2.

Work out the value of 𝑥 to 3 decimal places.

Work out the solution to 5 decimal places.

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