What is the discriminant of #4x^2-64x+145=-8x-3# and what does that mean?
The discriminant of an equation tells the nature of the roots of a quadratic equation given that a,b and c are rational numbers.
The discriminant of a quadratic equation
The discriminant actually tells you the nature of the roots of a quadratic equation or in other words, the number of x-intercepts, associated with a quadratic equation.
Now we have an equation;
First transform it to standard form of the quadratic equation.
Now compare the above equation with quadratic equation
Hence the discriminant (D) is given by;
Therefore the discriminant of a given equation is 48.
Here the discriminant is greater than 0 i.e.
Note: If the discriminant is a perfect square, the two roots are rational numbers. If the discriminant is not a perfect square, the two roots are irrational numbers containing a radical.