Question

Find the zeroes of the polynomial and verify the relationship between zeroes and coeffiecients.
X^2-6x+9

Answer 1

Step-by-step explanation:

In the given polynomial x2−6x+9,

The first term is x2 and its coefficient is 1.

The middle term is −6x and its coefficient is −6.

The last term is a constant term 9.

Multiply the coefficient of the first term by the constant 1×9=9.

We now find the factor of 9 whose sum equals the coefficient of the middle term, which is −6 and then factorize the polynomial x2−6x+9 as shown below:

 

x2−6x+9=x2−3x−3x+9=x(x−3)−3(x−3)=(x−3)(x−3)

Therefore, x2−6x+9=(x−3)(x−3).

so the zero of the polynomial is 3.