Question

find the Zero of the polynomial x square -9

Answer 1

Polynomial x² - 8x + k = 0

Since, we know that

The sum of the roots of polynomial of degree 2 is equal to the - b/a.

Let,the roots of polynomial be m and n,

Then, m+ n = -b/a.

m + n = - (-8)/1

m + n = 8 …(1)

NOW,

According to the quastion

m = n + 2 …(2)

Solving the equation (1) and (2), we get

n = 3

And m = 5

Therefore, roots of the polynomial are 5 and 3.

Hence, the required polynomial is x² - 8x + 15.

Answer 2

$\textbf{Heya}$

${x}^{2} - 9 \\ \\ = {x}^{2} - {3}^{2} \\ \\ using \: identity \: {a}^{2} - {b}^{2} = (a - b)(a + b) \\ \\ = (x - 3)(x + 3) \\ \\ now \\ \\ x - 3 = 0 \: and \: x + 3 = 0 \\ \\ x = 3 \: and \: x = - 3$



Hope this helps you.