To find the values of the coefficients and constant term for the quadratic equation [tex]\(0 = 4 - 7x^2 + x\)[/tex], we need to rewrite it in standard form. The standard form of a quadratic equation is:
[tex]\[ ax^2 + bx + c = 0 \][/tex]
Let's rewrite the given equation:
[tex]\[ 0 = 4 - 7x^2 + x \][/tex]
First, let's rearrange the terms on the right-hand side to match the standard form [tex]\( ax^2 + bx + c \)[/tex]:
[tex]\[ 0 = -7x^2 + x + 4 \][/tex]
Now we can identify the coefficients [tex]\(a\)[/tex], [tex]\(b\)[/tex], and the constant term [tex]\(c\)[/tex]:
- The coefficient of [tex]\(x^2\)[/tex] is [tex]\(a\)[/tex].
- The coefficient of [tex]\(x\)[/tex] is [tex]\(b\)[/tex].
- The constant term is [tex]\(c\)[/tex].
From the rearranged equation [tex]\( -7x^2 + x + 4 = 0 \)[/tex]:
- The coefficient [tex]\(a\)[/tex] is [tex]\(-7\)[/tex].
- The coefficient [tex]\(b\)[/tex] is [tex]\(1\)[/tex].
- The constant term [tex]\(c\)[/tex] is [tex]\(4\)[/tex].
So the values are:
[tex]\[
\begin{array}{l}
a = -7 \\
b = 1 \\
c = 4 \\
\end{array}
\][/tex]
