Let's analyze the quadratic expression [tex]\(7 \sqrt{2} x^2 - 10x - 4 \sqrt{2}\)[/tex]. To understand the different components of this expression, let's break it down into its coefficients and constant term.
A quadratic expression of the form [tex]\(ax^2 + bx + c\)[/tex] has three key components:
1. Coefficient of [tex]\(x^2\)[/tex], denoted as [tex]\(a\)[/tex]
2. Coefficient of [tex]\(x\)[/tex], denoted as [tex]\(b\)[/tex]
3. Constant term, denoted as [tex]\(c\)[/tex]
For the given expression [tex]\(7 \sqrt{2} x^2 - 10 x - 4 \sqrt{2}\)[/tex]:
1. The coefficient of [tex]\(x^2\)[/tex] is [tex]\(7 \sqrt{2}\)[/tex].
2. The coefficient of [tex]\(x\)[/tex] is [tex]\(-10\)[/tex].
3. The constant term is [tex]\(-4 \sqrt{2}\)[/tex].
Now, let's determine the numerical values of these components:
1. The coefficient [tex]\(a = 7 \sqrt{2}\)[/tex] approximately equals [tex]\(9.899494936611665\)[/tex].
2. The coefficient [tex]\(b = -10\)[/tex].
3. The constant term [tex]\(c = -4 \sqrt{2}\)[/tex] approximately equals [tex]\(-5.656854249492381\)[/tex].
These values are the accurate representations of the coefficients and the constant term in the quadratic expression when the square roots are evaluated:
Thus, we can identify:
- [tex]\(a = 9.899494936611665\)[/tex]
- [tex]\(b = -10\)[/tex]
- [tex]\(c = -5.656854249492381\)[/tex]
These values define the quadratic expression [tex]\(7 \sqrt{2} x^2 - 10 x - 4 \sqrt{2}\)[/tex].
