The cubic polynomial R(x)=x3−4x+1 is suspected to have a zero near x=1.3.
(i) Find R(1.3) correct to two decimal places.
(ii) On the basis of your answer in part (i), decide whether x=1.3 can be accepted as a zero of R(x) correct to two decimal places. Give a short reason for your decision.
(iii) If x=1.3 is not an exact zero, explain what further step you would suggest to locate the zero more accurately (no calculation needed).