Certainly! Let's address each question step-by-step:
### Question 1: What is the quadratic term in the equation [tex]\( x^2 = 3x - 1 \)[/tex] ?
The given equation is [tex]\( x^2 = 3x - 1 \)[/tex].
To identify the quadratic term, we recognize the term with [tex]\( x \)[/tex] raised to the power of 2.
Here, it is clearly [tex]\( x^2 \)[/tex].
Thus, the quadratic term is [tex]\( \boxed{x^2} \)[/tex].
### Question 2: What is the numerical value of [tex]\( a \)[/tex] in the equation [tex]\( x(x - 4) = 14 \)[/tex] ?
First, expand the given equation:
[tex]\[ x(x - 4) = 14 \][/tex]
[tex]\[ x^2 - 4x = 14 \][/tex]
Next, reformat this into a standard quadratic equation form [tex]\( ax^2 + bx + c = 0 \)[/tex]:
[tex]\[ x^2 - 4x - 14 = 0 \][/tex]
In a quadratic equation of the form [tex]\( ax^2 + bx + c = 0 \)[/tex]:
- The coefficient of the [tex]\( x^2 \)[/tex] term is [tex]\( a \)[/tex].
Looking at the equation [tex]\( x^2 - 4x - 14 = 0 \)[/tex], we see that the coefficient of [tex]\( x^2 \)[/tex] is [tex]\( 1 \)[/tex].
Therefore, [tex]\( a = \boxed{-4} \)[/tex].
### Question 3: What is the constant term in the quadratic equation [tex]\( 7x^3 = -x^2 \)[/tex] ?
Rewriting the given equation:
[tex]\[ 7x^3 + x^2 = 0 \][/tex]
To identify the constant term, we normalize the equation into the form [tex]\( ax^2 + bx + c = 0 \)[/tex].
First, let's rearrange the equation from [tex]\( 7x^3 + x^2 = 0 \)[/tex]:
- There is no term with [tex]\( x \)[/tex] or a constant term without [tex]\( x \)[/tex].
So, the constant term is [tex]\( c = 0 \)[/tex].
Thus, the constant term in the equation is [tex]\( \boxed{0} \)[/tex].
### Summary of answers:
1. The quadratic term is [tex]\( \boxed{x^2} \)[/tex].
2. The numerical value of [tex]\( a \)[/tex] is [tex]\( \boxed{-4} \)[/tex].
3. The constant term is [tex]\( \boxed{0} \)[/tex].
