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Solution


Q.

For the polynomial r(x) = x² – 4x + 4, which of the following statements are correct about its graph and zeros

 

 

(i) The graph touches the x-axis at x = 2.
(ii) The graph intersects the x-axis at x = 2.
(iii) The polynomial is equivalent to (x – 2)².
(iv) The vertex of the graph is at the point (2, 0).

 

Choose the correct option from the following:
1 (i), (iii) and (iv)  
2 (ii) and (iii)  
3 (i), (ii) and (iv)  
4 (i) and (iv)  

Ans.

(1)

Given polynomial r(x) can be rewritten as (x – 2)², indicating a repeated zero at x = 2. The graph touches the x-axis at this point and does not cross it. The vertex of the graph is at point (2, 0).