Question

Find the zeros of cubic polynomials (i) – x3 (ii) x2 – x3 (iii) x3 – 5x2 + 6x without drawing the graph of the polynomial.

Answer 1

(i) - x³
-x³ = 0
x = 0, hence zeros of -x³ is 0

(ii) x² - x³
x² - x³ = 0
x²(1 - x) = 0
x² = 0 or, (1 - x ) = 0.
x = 0 , 1
hence, zeros of x² - x³ are 0 , 1

(iii) x³ - 5x² + 6x
x³ - 5x² + 6x = 0
x(x² - 5x + 6) = 0
x(x - 2)(x - 3) = 0
x = 0, 2, 3
hence, zeros of x³ - 5x² + 6x are 0, 2, 3

Answer 2

In the attachment I have answered this problem.  Concept:  A real number 'a' is said to be a zero of the polynomial f(x) if f(a) = 0.  See the attachment for detailed solution.