Question

How many zeros does the polynomial (x – 3)2 – 4 have? Also, find its zeroes.
✧✧✧

Answer 1

Answer:

Given equation is (x – 3)^2– 4

Now, expand this equation.

=> x^2+ 9 – 6x – 4

= x^2– 6x + 5

As the equation has a degree of 2, the number of zeroes will be 2.

Now, solve x^2– 6x + 5 = 0 to get the roots.

So, x^2– x – 5x + 5 = 0

=> x(x – 1) -5(x – 1) = 0

=> (x – 1)(x – 5) = 0

x = 1, x = 5

So, the roots are 1 and 5.

Answer 2

Answer:

(x - 3)² - 4

= x² - 6x + 9 - 4

= x² - 6 x + 5

= (x² - 5x - x + 5)

= x(x - 5) - 1(x-5)

= (x-5)(x-1)

For f(x)=0 , x=5,1

So the function has 2 zeroes 1 and 5.