Segmentation of the left ventricle and quantification of various cardiac contractile functions is crucial for the timely diagnosis and treatment of cardiovascular diseases. Traditionally, the two tasks have been tackled independently. Here we propose a convolutional neural network based multi-task learning approach to perform both tasks simultaneously, such that, the network learns better representation of the data with improved generalization performance. Probabilistic formulation of the problem enables learning the task uncertainties during the training, which are used to automatically compute the weights for the tasks. We performed a five fold cross-validation of the myocardium segmentation obtained from the proposed multi-task network on 97 patient 4-dimensional cardiac cine-MRI datasets available through the STACOM LV segmentation challenge against the provided gold-standard myocardium segmentation, obtaining a Dice overlap of $0.849 \pm 0.036$ and mean surface distance of $0.274 \pm 0.083$ mm, while simultaneously estimating the myocardial area with mean absolute difference error of $205\pm198$ mm$^2$.