Question

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

Answer 1

Polynomial is p(x)=x

3

+13x

2

+32x+20

one of the zero is x=−2

One factor of p(x) is (x+2)

⇒ Polynomial becomes p(x)=(x+2)(x

2

+11x+10) factoring the quadratic, by middle term spletting

⇒ p(x)=(x+2)(x

2

+10x+x+10)

=(x+2)[x(x+10)+1(x+10)]

=(x+2)[(x+10)(x+1)]

⇒ Other factor are x+10 and x+1

Zeros are x=−10 and x=−1

⇒ All the zeroes of polynomial p(x) are −1,−2 and −10

Hope it helps you

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Answer 2

Step-by-step explanation:

Solution:

Given equation is (x – 3)2 – 4

Now, expand this equation.

=> x2 + 9 – 6x – 4

= x2 – 6x + 5

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

Now, solve x2 – 6x + 5 = 0 to get the roots.

So, x2 – x – 5x + 5 = 0

=> x(x – 1) -5(x – 1) = 0

=> (x – 1)(x – 5) = 0

x = 1, x = 5