The discriminant of a quadratic equation is b^2-4ac.
Two
Practice makes perfect
In a quadratic equation, both a and b are greater than 0 and c is less than 0.
ax^2+bx+c=0We want to determine the number of solutions of the equation. To do so, we will use the discriminant of the quadratic equation. In the Quadratic Formula, b^2-4ac is the discriminant.
ax^2+bx+c=0
⇕
x=- b±sqrt(b^2-4ac)/2a
Let's determine the sign of the discriminant.
b^2_(>0) -4ac_(>0) >0
Since a square of a number is positive and the product of two negative numbers is positive, the discriminant of the equation is always positive. This means that the equation has two real solutions.
