b We want to use the discriminant of the given quadratic equation to determine the number and type of the roots. If we do not want to know the exact values of the roots, we only need to work with the discriminant. From Part A, we know that the discriminant of the given equation is 0.
Equation:& x^2-6x=- 9
Discriminant:& 0
Since the discriminant is equal to zero, the quadratic equation has one real root.
c We will use the Quadratic Formula to find the exact solutions of the given equation.
x=- b±sqrt(b^2-4 a c)/2 a
Recall that we have already identified the values of a, b, and c in Part A, as well as the discriminant, b^2-4ac.
a= 1, b= - 6, c= 9
Discriminant:
Let's substitute these values into the Quadratic Formula.
Since adding or subtracting zero does not change the value of a number, the numerator will simplify to 6. Therefore, we will get only one value of x.
x=6/2 ⇔ x=3
Using the Quadratic Formula, we found that the solution of the given equation is x=3.
