What is the sum of the roots of the equation 𝑥 squared minus 24 equals zero?
Well, what we’re trying to find is the sum of our roots. Well, the roots of the equation, also the solutions of the equation. So what we’re gonna do is solve our equation, find our solutions. And then, we’re gonna add them together. So if we have 𝑥 squared minus 24 equals zero and the first thing we’d need to do is add 24 to both sides of the equation. That’s because we want the 𝑥 term on its own on the left-hand side. So this is gonna give us 𝑥 squared is equal to 24.
So now, we think, right what do we want to do. Well, we wanna a single 𝑥. We don’t want 𝑥 squared. So what we’re gonna need to do is take the inverse of squaring. So that’s gonna be square root. And we’re gonna square root both sides of the equation. Well, when we do this, this is gonna give us two solutions for 𝑥 because we could say that 𝑥 is equal to positive or negative root 24. And that’s because if we think about if we had root 24 multiplied by root 24, that would give us 24. And negative root 24 multiplied by negative root 24, that would also give us 24.
Now, I’m not gonna actually work out the value of root 24 because we don’t need to in this question. We just need to now add our roots together. Well, if we add our roots together, we’re gonna get negative root 24 add root 24. And this is gonna be equal to zero because they’re gonna cancel each other out.
So therefore, we can say that the sum of the roots of the equation 𝑥 squared minus 24 equals zero is zero.