Sure! Let's start by rewriting the given equation in the standard quadratic form. The given equation is:
[tex]\[ x^2 - 10 = 0 \][/tex]
The standard form of a quadratic equation is:
[tex]\[ ax^2 + bx + c = 0 \][/tex]
To match the given equation to this form, we can compare:
1. The term [tex]\( x^2 \)[/tex] appears directly, so the coefficient [tex]\( a \)[/tex] is the multiplier of [tex]\( x^2 \)[/tex]. In this case, [tex]\( a = 1 \)[/tex].
2. The given equation does not have an [tex]\( x \)[/tex] term, so the coefficient [tex]\( b \)[/tex] of the [tex]\( x \)[/tex] term is [tex]\( 0 \)[/tex], i.e., [tex]\( b = 0 \)[/tex].
3. The constant term [tex]\( c \)[/tex] is the standalone number. Here, we have [tex]\( -10 \)[/tex], so [tex]\( c = -10 \)[/tex].
Putting it all together, we get the equation in the standard form:
[tex]\[ 1 \cdot x^2 + 0 \cdot x - 10 = 0 \][/tex]
Thus, the values of [tex]\( a \)[/tex], [tex]\( b \)[/tex], and [tex]\( c \)[/tex] are:
[tex]\[ a = 1, \quad b = 0, \quad c = -10 \][/tex]
