Question

How do you find the real zeros of a polynomial function on an Nspire?

Answer 1

Hint: Nspire is a graphing calculator which is used to solve complex mathematics equations and functions. To find the zeros, we first have to select the “Algebra” menu and choose the “Find roots of polynomial” option. There on entering the degree, nature of roots, and the coefficients of the polynomial function, we will get the required zeros of the polynomial function.

Complete step by step solution:
For finding out the roots of a polynomial function, we first need to determine the degree of the polynomial function. The degree of a polynomial function is defined as the highest power of the variable in the terms of which is the polynomial function, which is usually x. Let us suppose that the polynomial function whose zeros are to be determine is given by
$\Rightarrow p\left( x \right)={{x}^{2}}-5x+6$
We can see that the above polynomial function is x whose highest power is equal to two. Therefore, the above polynomial has a degree equal to two.
Now, having determined the degree of the polynomial function, we have to click on the menu button at the top-right side of the Nspire and select the “Algebra” menu from the options. To the right of the algebra menu, select the polynomial tools option. Then select the option “Find roots of polynomials”. Then you will have to enter two values, first is the degree of the polynomial, and second is the Roots. In the Degree option, you will have to enter the degree of the polynomial, which is two in the case of our example. And in the Roots option, you will have to select the nature of roots, real or complex. In the case of our example, we will choose the real option.
After this, you will be asked to enter the coefficients of ${{x}^{2}}$, $x$ and the constant term of the polynomial. In our case, we will enter the coefficients $1$, $-5$ and $6$. After this, we will hit the “Enter” button and we will obtain the solutions in the parenthesis. For the polynomial ${{x}^{2}}-5x+6$ we will obtain the roots as $\left\{ 2,3 \right\}$.
Hence, we have finally learnt to find the zeros of a polynomial function on an Nspire.

Note: We can also use the solve option inside the algebra menu for obtaining the zeros. After choosing the solve option, we need to enter the polynomial function and equate it to zero inside the parenthesis represented on the screen as $\text{solve}\left( {} \right)$. Then we also need to enter the variable of the polynomial after a comma. For the polynomial ${{x}^{2}}-5x+6$, we will type $\text{solve}\left( {{x}^{2}}-5x+6=0,x \right)$ and then hit enter to finally obtain the solutions.