<prompt> Find the roots of the polynomial equation 5x2 2x -3 0.  <response>: To find the roots of the given polynomial equation 5x2 2x -3 0, we can use the quadratic formula: x -b b2-4ac2a. Substituting the values of a5, b2, and c-3 into the formula gives:x -2 22 - 4 5 -3 25 -2 4 60 10 -2 64 10 -2 8 10So, the two roots of the polynomial are:x -2 8 10 610 0.6 and x -2 - 8 10 -1010 -1So, the solutions to the polynomial equation 5x2 2x -3 0 are x 0.6 and x -1. 