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Chapter 1: Problem 1

Solve each equation in Exercises \(1-14\) by factoring. $$x^{2}-3 x-10=0$$

Short Answer

Expert verified
The roots of the given equation \(x^{2}-3 x-10=0\) are \(x=5\) and \(x=-2\)

Step by step solution

01

Identify the equation

The equation given in the exercise is \(x^{2}-3 x-10=0\)
02

Factorize the quadratic equation

The equation can be factorized by finding two numbers such that their sum is -3 (the coefficient of \(x\)) and their product is -10 (the constant term). The numbers that satisfy these conditions are -5 and 2 as -5*2 = -10 and -5 + 2 = -3. So, the factorized form of the equation is \((x-5)(x+2)=0\)
03

Solve for \(x\)

If the product of two numbers equals zero, at least one of these numbers must be zero. Therefore, setting the two factors equal to zero, we find \(x-5=0\) or \(x+2=0\). Solving these equations gives us the roots \(x=5\) and \(x=-2\)

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Most popular questions from this chapter

In Exercises \(29-44,\) perform the indicated operations and write the result in standard form. $$\frac{-8+\sqrt{-32}}{24}$$

In Exercises \(29-44,\) perform the indicated operations and write the result in standard form. $$\frac{-15-\sqrt{-18}}{33}$$

Solve each rational inequality in Exercises \(29-48,\) and graph the solution set on a real number line. Express each solution set in interval notation. $$ \frac{x-4}{x+3}>0 $$

Solve each rational inequality in Exercises \(29-48,\) and graph the solution set on a real number line. Express each solution set in interval notation. $$ \frac{x+5}{x-2}>0 $$

In Exercises \(29-44,\) perform the indicated operations and write the result in standard form. $$\frac{-6-\sqrt{-12}}{48}$$
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