Solve a quadratic by applying the square root method

The video tutorial explains how to solve the equation y = X^2 - 16 using two methods: factoring by the difference of squares and the square root method. Initially, it demonstrates factoring by setting the equation to zero and rewriting it as (X - 4)(X + 4) = 0, leading to solutions X = 4 and X = -4. The tutorial then introduces the square root method, which involves isolating X^2, adding 16 to both sides, and taking the square root to find X = ±4. Both methods yield the same solutions, highlighting the versatility of the square root method for equations in the form of AX^2 + C.

What is the factored form of the equation y = X^2 - 16 using the difference of two squares?

• (X - 4)(X + 4)

• (X - 8)(X + 2)

• (X - 2)(X + 8)

• (X - 16)(X + 1)

Which method can be used to solve any equation in the form of aX^2 + C?

• Factoring by grouping

• Synthetic division

• Completing the square

• Square root method

What is the first step in solving an equation using the square root method?

• Set the equation equal to zero

• Factor the equation

• Add a constant to both sides

• Multiply both sides by a constant

When using the square root method, why must both positive and negative roots be considered?

• Because squaring a number results in a positive value

• Because it simplifies the equation

• Because it ensures all possible solutions are found

• Because the equation might have complex roots

What are the solutions to the equation X^2 = 16 using the square root method?

• X = 0

• X = ±4

• X = ±16

• X = 8