In this example, we'll solve
the quadratic equation x squared
minus 10x plus 25 equals 0.
Remember, the quadratic formula
says that the solutions to ax
squared plus bx plus c equals
0 are given by the formula
negative b plus or
minus the square root
of b squared minus
4ac all over 2a,
where our a, b, and c
come from the coefficients
of our equation.
In this example, a is 1, b
is negative 10, and c is 25.
So we get that our
solutions are given
by negative negative
10 plus or minus
the square root of negative 10
squared minus 4 times 1 times
25.
Negative negative 10 is 10.
Negative 10 squared is 100.
And 4 times 1 times
25 is also 100.
So we get 10 plus or
minus the square root
of 100 minus 100 over 2.
But 100 minus 100 is 0, so
we have 10 plus or minus
the square root of 0 over 2.
And the square root
of 0 is still 0.
So we have 10 plus
or minus 0 over 2.
Well, 10 plus 0 is 10
and 10 minus 0 is 10.
So we get that our solutions
are 10 over 2 and 10 over 2.
In other words, 5 and 5.
So the solutions to x squared
minus 10x plus 25 equals 0
are x equals 5 and x equals 5.
Remember, since
5 is repeated, we
say that x equals 5 is a
zero of multiplicity 2.
Notice that the reason
the two roots are the same
is because adding
0 and subtracting 0
gives the same number.
And having plus or minus
0 was a result of b
squared minus 4ac equaling 0.
