What is the quadratic equation whose roots are -6 and 6, and whose leading coefficient is 1?

Answer 1

Hey!

According to what you wrote, you're looking for a quadratic equation that has the roots: -6 and 6. The leading coefficient is 1. Since we know it is a quadratic equation we know it has x². Since the leading coefficient is 1 we know that it is just x² . Now that we've figured that out, let's focus on using the roots.

When we're talking about roots, roots in a regular quadratic equation are when the equation = 0.

coefficient x (root 1) x (root 2) = 0.

So let's figure out how we can get 0. Since it is multiplication we know that there must be something that equals 0, because 0 times anything = 0. We also know the leading coefficient is 1.

Which means :

1 *(root 1) * (root 2) = 0

root 1: what number + (-6) =0 ? number: 6

root 2: what number + (6) = 0? number: -6

1*(x+6)*(x-6) = 0

Now, let's multiply everything:

x*x = x²

x*(-6) = -6x

x*6 = 6x

6*(-6) = (-36)

Lastly, let's combine everything together:

x² -6x + 6x -36

Simplifies to:

x²-36 = 0 (where did the zero come from? quadratic equations always equal to zero. That's how we found the roots of the problem).

Answer: x²-36 = 0

I hope this helps!

Best of wishes!

Answer 2

(x-6)*(x+6) = x² -36

The roots are the negatives of the factors.