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Chapter 1: Problem 23

Find the zeros of the function algebraically. $$ f(x)=2 x^{2}-7 x-30 $$

Short Answer

Expert verified
The zeros of the function are \(x = -5/2\) and \(x = 6\).

Step by step solution

01

Set the function equal to zero

We set the function \(f(x) = 2x^{2} - 7x - 30\) equal to zero. This gives us: \[2x^{2} - 7x - 30 = 0\]
02

Factor the equation

We can factorize the equation \(2x^{2} - 7x - 30 = 0\). This gives us: \[(2x + 5)(x - 6) = 0\]
03

Solve for x

Now we can set each factor equal to zero and solve for \(x\). That gives us: \[2x + 5 = 0 \Rightarrow x = -5/2\] and \[x - 6 = 0 \Rightarrow x = 6\].

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Most popular questions from this chapter

Write a sentence using the variation terminology of this section to describe the formula. Volume of a sphere: \(V=\frac{4}{3} \pi r^{3}\)

Mathematical models that involve both direct and inverse variation are said to have _____ variation.

The joint variation model \(z=k x y\) can be described as " \(z\) varies jointly as \(x\) and \(y\)," or \(" z\) is_____ _____ to \(x\) and \(y.\) "

(a) find the inverse function of \(f\), (b) graph both \(f\) and \(f^{-1}\) on the same set of coordinate axes, (c) describe the relationship between the graphs of \(f\) and \(f^{-1}\), and (d) state the domain and range of \(f\) and \(f^{-1}\). $$ f(x)=-\frac{2}{x} $$

Determine whether the function has an inverse function. If it does, find the inverse function. $$ f(x)=\sqrt{2 x+3} $$
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