Answer:

(c) x² - 2

Step-by-step explanation:

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Answer:

Step-by-step explanation:To find the quadratic polynomial with roots

2

2 and

0

0, we use the factored form of a quadratic polynomial:

�

(

�

)

=

�

(

�

−

�

1

)

(

�

−

�

2

)

P(x)=a(x−r

1

​

)(x−r

2

​

)

where

�

1

r

1

​

 and

�

2

r

2

​

 are the roots of the polynomial.

Given that the roots are

2

2 and

0

0, we can write the polynomial as:

�

(

�

)

=

�

(

�

−

2

)

(

�

−

0

)

P(x)=a(x−2)(x−0)

Now, expand and simplify:

�

(

�

)

=

�

(

�

−

2

)

�

P(x)=a(x−2)x

�

(

�

)

=

�

�

2

−

2

�

�

P(x)=ax

2

−2ax

Now, compare this with the given options:

(a)

�

2

−

2

�

x

2

−2x - This matches with our expression, so

�

=

1

a=1.

(b)

�

2

−

2

�

+

1

x

2

−2x+1 - This does not match.

(c)

�

2

−

2

x

2

−2 - This does not match.

(d)

�

2

−

4

x

2

−4 - This does not match.

Therefore, the correct quadratic polynomial is

�

2

−

2

�

x

2

−2x, and the correct option is (a).