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Chapter 11: Problem 98

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. Because I want to solve \(25 x^{2}-169=0\) fairly quickly, I'll use the quadratic formula.

Short Answer

Expert verified
The statement makes sense as even though the \(bx\) term is not explicitly present, the equation is still a quadratic equation and thus, can be solved using the quadratic formula.

Step by step solution

01

Identify the type of equation

Start by identifying the type of given equation. Here, the equation \(25x^{2}-169=0\) seems to be in quadratic form but lacking the \(bx\) term.
02

Explaining the Structure of Quadratic Equations

Recognize that the standard form of a quadratic equation is \(ax^{2} + bx + c = 0\). In case, \(b=0\) and \(c\) is negative, the equation is still a quadratic equation, but a special case of it.
03

Apply the Quadratic formula and reason

Even though there is no \(bx\) term, one can still apply the quadratic formula \(x = \frac{-b \pm \sqrt{b^{2}-4ac}}{2a}\). Since \(b=0\) and \(c=-169\), the formula becomes \(x = \sqrt{\frac{169}{25}}\), which can be solved readily. Therefore, the statement 'Because I want to solve \(25x^{2}-169=0\) fairly quickly, I'll use the quadratic formula.' makes sense because it can lead to a solution.

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Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. I need to find a square root to determine the discriminant.
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