(Q20)Find the zeros of cubic polynomials
(i) - x3(ii)x2 - x3(iii)x3 - 5x2+6x

Answer:

(i)Given polynomial is y= - x3

f(x)= - x3;f(x)=0

x3=

x=

Zero of the polynomial f(x) is only one i.e,.

(ii)Given that y=x2 - x3

f(x)=x2(1-x)

f(x)=0

x2(-x)=0

x2=0 and -x=0

x=0 and x=

The zeros of the polynomial f(x) are two 0 and .

(iii)Given that x3 - 5x2+6x

Let f(x)=x3 - 5x2+6x

x(x2 - 5x+6)

x(x2 -x-3x+6)

x[x(x-) - 3(x-)]

x(x-)(x-3)

The zeros of the polynomial f(x) are x=0 and x= and x=3.