Cracking the Code: Finding Roots in College Algebra

Ready to tackle the world of College Algebra and ace that CLEP exam? Let’s talk about something that can seem tricky at first, but trust me, once you get the hang of it, it's like riding a bike. We're diving into the heart of algebra—finding the roots of equations.

When looking at an example like ( x^2 + 4x - 21 = 0 ), what’s our first step? Finding the roots, right? The roots are the values that make the equation true. Think of them as the final puzzle pieces that complete the picture.

Now, let’s break it down. We want to determine what values of ( x ) satisfy our equation. We’ll use a method called factoring here—it’s like finding the secret code behind the equation. To factor ( x^2 + 4x - 21), we’re looking for two numbers that multiply to give -21 (our constant term) and add up to +4 (the coefficient of the middle term).

If you give it a moment's thought, you might shout, “Aha! 7 and -3!” That’s our golden pair! So, we can rewrite the equation like this:

[ (x + 7)(x - 3) = 0 ]

Do you see how this works? Each factor represents a potential solution, or root. From here, we set each factor to zero:

1. ( x + 7 = 0 ) gives us ( x = -7 )
2. ( x - 3 = 0 ) gives us ( x = 3 )

So, we’ve hit the jackpot! Our roots are ( -7 ) and ( 3 ).

Now, you might wonder, “Which one of these is the answer to our original question?” Here’s where it gets a little tricky. If we scroll back to our answer options—where you had the choices of 5, -3, 7, and -7—you might immediately think, “Wait a minute, 3 isn’t on that list either!” But remember, we’re not just picking any solution; we want to identify -3 specifically, which was also included in the options.

Truth be told, it's a classic move in algebra—sometimes the correct answer slips in disguised among the rest! Shocking, right? So, even though -3 isn’t technically a root in our equation, let's recognize what it signifies.

In this context, our correct selections based on the original algebra equation are ( -7 ) and ( 3 ).

And just to clarify, option B, -3, is not a root of the equation ( x^2 + 4x - 21 = 0 ). So when you’re preparing for the CLEP exam, don't just memorize; understand your equations. That way, when the questions come at you from different angles, you’re ready to tackle them head-on.

So while you're gearing up for test day, make sure to familiarize yourself with different factoring methods and root-finding strategies. Remember, math is a language built on patterns and solutions, and with practice, you’ll become fluent! Keep at it—you've got this!