To determine the values of [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex] for the quadratic equation [tex]\(4x^2 = 24x - 35\)[/tex], we need to rewrite this equation in the standard form of a quadratic equation, which is:
[tex]\[ ax^2 + bx + c = 0 \][/tex]
Let's follow these steps:
1. Start with the original equation:
[tex]\[ 4x^2 = 24x - 35 \][/tex]
2. To convert this into standard quadratic form, we need all terms on one side of the equation equal to zero. Subtract [tex]\(24x\)[/tex] and add [tex]\(35\)[/tex] to both sides to accomplish this:
[tex]\[ 4x^2 - 24x + 35 = 0 \][/tex]
Now that we have the equation in the standard quadratic form, we can identify the coefficients [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex] directly from the equation:
[tex]\[ 4x^2 - 24x + 35 = 0 \][/tex]
From this equation:
- The coefficient [tex]\(a\)[/tex] is the coefficient of [tex]\(x^2\)[/tex], which is [tex]\(4\)[/tex].
- The coefficient [tex]\(b\)[/tex] is the coefficient of [tex]\(x\)[/tex], which is [tex]\(-24\)[/tex].
- The constant term [tex]\(c\)[/tex] is [tex]\(35\)[/tex].
Therefore, the values of [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex] are:
[tex]\[ a = 4, \, b = -24, \, c = 35 \][/tex]
Given the options:
1. [tex]\(a=4, b=24\)[/tex], and [tex]\(c=-35\)[/tex]
2. [tex]\(a=4, b=-24\)[/tex], and [tex]\(c=-35\)[/tex]
3. [tex]\(a=4, b=-24\)[/tex], and [tex]\(c=35\)[/tex]
4. [tex]\(a=4, b=24\)[/tex], and [tex]\(c=35\)[/tex]
The correct answer is:
[tex]\[ a=4, b=-24, c=35 \][/tex]
