Question

Determine the discriminant, and then state the nature of the solutions. 9x^2-30x+25=0The discriminant tells us there is Answer

Answer 1

To answer this question, we need to remember was the discriminant of a quadratic equation means. The discriminant is given by the following formula:

`D=b^2-4ac`

The values of a, b, and c, are:

• a is the leading coefficient (or quadratic coefficient)

,

• b is the linear coefficient

,

• c is the constant-coefficient

We can see this in the general formula:

`ax^2+bx+c`

In this case, we have that the polynomial:

`9x^2-30x+25=0`

Then

• a = 9

,

• b = -30

,

• c = 25

If we use the formula of the discriminant, we have:

`D=b^2-4ac\Rightarrow D=(-30)^2-4(9)(25)=900-900=0`

When we have that the discriminant of the polynomial is equal to 0, then the parabola that represents the quadratic formula will have only one x-intercept. It has one real solution. However, this solution is a multiplicity, that is this solution is