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Solution


Q.

For the polynomial t(x) = x³ – 6x² + 11x – 6, which statements are true about its graph and zeros

(i) The polynomial has a zero at x = 1.
(ii) The polynomial has a zero at x = 2.
(iii) The graph of the polynomial intersects the x-axis at x = 3.
(iv) The polynomial can be factorised as (x – 1)(x – 2)(x – 3).

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

Ans.

(2)

At x = 1, t(1) = 1 – 6 + 11 – 6 = 0

So (x – 1) is a factor of t(x).

∴ t(x) = (x – 1)(x² – 5x + 6)

⇒ t(x) = (x – 1)(x – 2)(x – 3)

Factoring t(x) as (x – 1)(x – 2)(x – 3) reveals zeros at x = 1, 2, 3. The graph intersects the x-axis at these points.