Find in its simplest form the quadratic equation whose roots are eight square root 11 and negative square root 11.
In order to solve for this equation, we’re essentially working backwards from what we’re used to. So let’s go ahead and take these numbers, eight square root 11 and negative square root 11, and bring them over to the left-hand side of the equation. That way these little equations are equal to zero.
So these our factors, so we can rewrite them like this. And now we can use the distributive property and FOIL. First, you take 𝑥 times 𝑥 to get 𝑥 squared. Then we multiply 𝑥 times square root 1 to get 𝑥 square root 11. Then we take negative eight square root 11 times 𝑥, which is negative eight 𝑥 square root 11.
And then negative eight squared root 11 times square root 11. That is just negative eight times 11 because square root 11 times squared root 11 is 11. We can combine the two middle terms to be negative seven 𝑥 square root 11. And the negative eight times 11 is negative 88. So this will be our final equation.