solve 6x^3-13x^2+x+2=0 using a graphing calculator. then use your answer to write the given function in factored form. (do not use the factor theorem to factor this.) (6 marks)
How do you propose we show a "graphing calculator" solution on here ?
since choices of x+ ±1, ±2 are the obvious first guesses and x = 2 can be found to be a solution in a few seconds,
I then did a synthetic division to get
6x^3-13x^2+x+2=0
(x-2)(6x^2 - x - 1) = 0
(x-2)(3x+1)(2x-1) = 0
x = 2 or -1/3 or 1/2
To solve the equation 6x^3 - 13x^2 + x + 2 = 0 using a graphing calculator, you can follow these steps:
1. Enter the equation into the graphing calculator: 6x^3 - 13x^2 + x + 2 = 0.
2. Set the calculator to graph the equation.
3. Look for the x-intercepts on the graph. These are the points where the graph crosses the x-axis.
4. The x-intercepts represent the solutions of the equation. Read off the values of x where the graph intersects the x-axis.
Once you have the solutions from the graphing calculator, you can write the given function in factored form by using the solutions of the equation. Let's say the solutions from the graphing calculator are x = a, x = b, and x = c.
Then the factored form of the function would be:
(x - a)(x - b)(x - c) = 0.
Simply substitute the values of a, b, and c into this equation to get the factored form.