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Solution


Q.

Consider the polynomial p(x) = x³ – 3x² + 2x. Which of the following statements are true about its graph and zeros

(i) The polynomial has a zero at x = 0.
(ii) The polynomial has a zero at x = 1.
(iii) The graph touches the x-axis at x = 1.
(iv) The graph intersects the x-axis at x = 2.

 

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

Ans.

(3)

p(x) = x³ – 3x² + 2x⇒ p(x) = x(x² – 3x + 2)⇒ p(x) = x(x – 2)(x – 1)

Factoring p(x) gives x(x – 1)(x – 2), indicating zeros at x = 0, 1, and 2. The graph intersects the x-axis at these points.