To determine the values of [tex]\(A\)[/tex], [tex]\(B\)[/tex], and [tex]\(C\)[/tex] needed to write the quadratic equation in standard form, let’s follow these steps.
1. Identify the given equation:
The given equation is [tex]\(\frac{1}{4} x^2 + 5 = 0\)[/tex].
2. Understand the standard form of a quadratic equation:
The standard form of a quadratic equation is [tex]\(Ax^2 + Bx + C = 0\)[/tex], where [tex]\(A\)[/tex], [tex]\(B\)[/tex], and [tex]\(C\)[/tex] are constants.
3. Compare the given equation with the standard form:
Compare [tex]\(\frac{1}{4} x^2 + 5 = 0\)[/tex] with [tex]\(Ax^2 + Bx + C = 0\)[/tex].
4. Determine the coefficients [tex]\(A\)[/tex], [tex]\(B\)[/tex], and [tex]\(C\)[/tex]:
- The term [tex]\(\frac{1}{4} x^2\)[/tex] corresponds to [tex]\(Ax^2\)[/tex]. Therefore, [tex]\(A = \frac{1}{4}\)[/tex].
- There is no [tex]\(x\)[/tex] term in the equation, which means [tex]\(B = 0\)[/tex].
- The constant term is [tex]\(5\)[/tex], which corresponds to [tex]\(C\)[/tex]. Therefore, [tex]\(C = 5\)[/tex].
So we have:
[tex]\[
A = 0.25, \ B = 0, \ C = 5
\][/tex]
Given this information, let's check the provided choices:
- [tex]\(A = 1 ; B = 0 ; C = 20\)[/tex]: These values do not correspond to our identification.
- [tex]\(A = 1 ; B = 0 ; C = -5\)[/tex]: These values do not correspond either.
- [tex]\(A = \frac{1}{4} ; B = 5 ; C = 0\)[/tex]: These values are not correct since [tex]\(B=5\)[/tex] is incorrect.
None of the provided options match the correct values.
It's important to note the exact correct values:
[tex]\[
A = 0.25, \ B = 0, \ C = 5
\][/tex]
