In order to find this, calculate out the discriminant for each of the following equations. A quadratic equation always has two zeroes.(May be equal) The discriminant shows whether they are real or not. The discriminate formula is b squared minus four ac for quadratic equation in standard form ax squared plus bx plus c. The discriminant is the part of the quadratic formula underneath the square root symbol: b²-4ac. The discriminant (Δ or D) of any polynomial is in terms of its coefficients. Here are the discriminant formulas for a cubic equation and quadratic equation. This can save you spending ages trying to factorize when it won't work. We can use the formula under the radical, b2−4ac, called the discriminant, to determine the number of roots of solutions in a quadratic equation. The discriminant can be used to analyse the types of solutions to a quadratic equation without actually solving the equation.