Question

Draw the graph of the polynomial p(x)= x^2-6x+9 and find its zeroes

Answer 1

Question:

Draw the graph of the polynomial $p(x)= {x}^{2} - 6x + 9$ and find its zeroes.

Given:

1. $p(x)= {x}^{2} - 6x + 9$

To Find:

• Zero of the polynomial.

Solution:

Consider the provided polynomial:-

$p(x) = {x}^{2} - 6x + 9$

Now compare the provided equation with standard equation :- ${ax}^{2} + bx + C$

$a = 1, b = -6 \ and \ c = 9$

Substitute x = 3 in above equation

$\implies p(x) = {x}^{2} - 6x + 9$

$\implies p(x) = {3}^{2} - 6(3) + 9$

$\implies p(x) = 9 - 18 + 9$

$\implies p(x) = 18 - 18$

$\implies p(x) = 0$

Hence,

The zero(0) of the polynomial $p(x) = {x}^{2} - 6x + 9 = 3$

● The required graph is shown above: