Use the discriminant to determine how many real-number solutions the equation has.
36x2 - 12x + 1 = 0
How do I do this?
the discriminant is
b^2 - 4ac , namely the part under the √ sign of the quadratic formula
If it is positive, there are 2 different real solutions
if it is zero, there is one real answer
if it is negative, there are two complex solutions
If it is a perfect square, such as 36, there are 2 rational solutions.
so your discriminant
= 144 - 4(36)(1) = 0
mmmhhh?
so 36 is 6,6 so there are two solutions. Am I understanding this correctly
No, you aren't understanding it. The discriminant is zero, as reiuny has shown, so there is only one solution.
36x^2 - 12x + 1 = (6x -1)^2 = 0
Note that the polynomial is a perfect square. The only answer is x = 1/6
To determine the number of real-number solutions for the equation 36x^2 - 12x + 1 = 0 using the discriminant, you need to follow these steps:
1. Firstly, identify the coefficients of the quadratic equation. In this case, the coefficients are:
a = 36
b = -12
c = 1
2. Calculate the discriminant (denoted as Δ) using the formula:
Δ = b^2 - 4ac
Substituting the values from the coefficients, we have:
Δ = (-12)^2 - 4 * 36 * 1
= 144 - 144
= 0
3. Examine the value of the discriminant:
- If Δ > 0, the equation has two distinct real solutions.
- If Δ = 0, the equation has one real solution.
- If Δ < 0, the equation has no real solutions (complex solutions).
In this case, since Δ = 0, it means there is one real solution for the quadratic equation 36x^2 - 12x + 1 = 0.