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

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

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

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

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

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

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

A ball’s height is modeled by $h(t)=-4.9t^2+9.8t+1$, 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.

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

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

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

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

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