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Solution


Q.

Assertion (A): The graph of q(x) = x³ – 3x² + 3x – 1 does not intersect the x-axis.

Reason (R): The polynomial can be factored as (x – 1)³.
1 Both A and R are true, and R is the correct explanation of A  
2 Both A and R are true, but R is not the correct explanation of A  
3 A is true, but R is false  
4 A is false, but R is true  

Ans.

(4)

Given: q(x) = x³ – 3x² + 3x – 1 = (x – 1)³.
We know that if a polynomial p(x) contains a factor of the form (x – a)?, then the graph of p(x) will touch the x-axis and turn at (a, 0) if k is even, and will cross the x-axis at (a, 0) if k is odd.
Here, k = 3, so the graph of q(x) will cross the x-axis at x = 1.