Question Type 3: Solving for a given polynomial equation using technology Exercises

Use a calculator to determine the nature (real or complex) and approximate values of the roots of $x^3 + x + 1 = 0$ to three decimal places.

Use a calculator to approximate the real roots of $2x^3 + x^2 - 4x - 2 = 0$ to three decimal places.

Find all roots of $x^3 + 3x^2 + 3x + 1 = 0$ by recognizing it as a binomial expansion and verify with technology.

Determine, with the aid of technology, the number of real roots of $x^4 - 5x^2 + 4 = 0$ and find their approximate values.

Find the roots of the equation $x^3 - 7x - 6 = 0$ using an analytical method and verify the results.

Employ a CAS to solve $2x^4 - x^3 - 7x^2 + 3x + 2 = 0$ and list all roots to three decimal places.

Use technology to find all roots of $3x^3 - x^2 - 12x + 4 = 0$, giving exact values when possible and decimal approximations otherwise.

Use a graphing tool to approximate the real root of $5x^3 + x - 1 = 0$ in the interval $[0, 1]$ to four decimal places.

Determine, using a graphing calculator, all roots of $x^4 - x^3 - x^2 + x + 1 = 0$ and give their values to three decimal places.

Use a graphing calculator to find all real roots of the equation $5x^3 - 11x^2 - 9x + 9 = 0$ to two decimal places.

Use technology to approximate the roots of $x^3 - x^2 + x - 1 = 0$ and classify them as real or complex.

Use a computer algebra system to find all roots (real and complex) of $5x^3 - 11x^2 - 9x + 9 = 0$, expressing complex roots in $a+bi$ form.