Compute the value of discriminant and give the number of real solutions of the quadratic function. 4x^2 -5x+6=0 explain your steps.

For a quadratic equation of the form  , the solutions are given by the quadratic equation      the expression under the square root is called the discriminant.the discriminant is the expression      if  (positive) there will be two distinct  real solutions.if  , there will be one distinct  real solution.if  (negative), there will be no real solutions. (cannot take square root of a negative number to get real solutions.)======for  , in accordance with the quadratic formula, we have      so the discriminant is      we see that the discriminant is negative.therefore, there are zero real solutions.