Exercises for Question Type 6: Calculating roots of polynomial equations using technology

Question 1

Skill question

Use technology to find the roots of $x^{2} + 2 x - 7 = 0$ . Give answers to 3 significant figures.

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Question 2

Skill question

Use a calculator’s polynomial solver to find all roots of $2 x^{2} + 10 x + 12 = 0$ .

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Question 3

Skill question

Find all (possibly complex) roots of $3 x^{2} + 2 x + 5 = 0$ using a calculator’s polynomial solver. Express answers to 3 s.f. in $a + bi$ form.

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Question 4

Skill question

Find all roots of $x^{3} + x^{2} + x + 1 = 0$ using technology. State real and complex roots.

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Question 5

Skill question

Use a calculator to solve $- 4 x^{2} + 7 x - 3 = 0$ . [2 marks]

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Question 6

Skill question

Solve $0.5 x^{3} - 3.5 x^{2} + 6 x - 2 = 0$ using a cubic solver. Give all roots to 3 s.f.

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Question 7

Skill question

A ball’s height is modeled by $h (t) = - 4.9 t^{2} + 9.8 t + 1$ , where $h$ is in meters and $t$ is in seconds. Use a polynomial solver to find when it hits the ground ( $h = 0$ ). Give the physically relevant time to 2 decimal places.

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Question 8

Skill question

Solve $2 x^{3} - 3 x^{2} - 11 x + 6 = 0$ using a calculator’s cubic solver.

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Question 9

Skill question

Find all roots of $x^{3} - 3 x^{2} - 13 x + 15 = 0$ using a polynomial solver.

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Question 10

Skill question

Use a polynomial solver to find all roots of $x^{3} - 6 x^{2} + 11 x - 6 = 0$ .

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Question 11

Skill question

Use technology to find all real roots of $x^{3} - 4 x + 1 = 0$ . Give your answers to 3 decimal places.

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Question 12

Skill question

Solve $1.5 x^{2} - 4.5 x + 3 = 0$ using a polynomial solver.

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IB Mathematics Applications & Interpretation Question Type 6: Calculating Roots of Polynomial Equations Using Technology Exercises