This is a free lesson from our course in Algebra I
In this lesson, you'll learn how to calculate and interpret the discriminant in the quadratic formula.A quadratic equation with real or complex coefficients has two solutions, called roots. These two solutions may or may not be distinct, and they may or may not be real. The roots are given by the quadratic formula:
x = -b (b2 – 4ac) / 2a
where the symbol "" indicates that both
-b + (b2 – 4ac) / 2a
and
-b - (b2 – 4ac) / 2a
are solutions for x.
(More text below video...)
(Continued from above) The expression underneath the square root sign is called the discriminant of the quadratic equation, and is often represented using an upper case Greek Delta: D= b2 – 4ac A quadratic equation with real coefficients can have either one or two distinct real roots, or two distinct complex roots. In this case the discriminant determines the number and nature of the roots. There are three cases:
• if D = 0, the discriminant
is zero, that means there is only one real number solution.
• if D > 0, the discriminant
is a positive number, that means there are two distinct real number solutions.
• if
D < 0 i.e. negative,
there are two distinct roots, each of which is a complex number. A complex number is of the form a + ib;
where and b are real numbers and i is the imaginary number with the property i2
= -1. E.g. (2 + -36)
is a complex number.
Thus the roots are distinct if and only if the discriminant is non-zero, and the roots are real if and only if the discriminant is non-negative.
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(b2 – 4ac) / 2a
-36)
is a complex number.