Finding Zeros and Solving Quadratics

The video tutorial explains how to find the zeros of a function by setting the function equal to zero and solving for x. It involves substituting values, factoring the expression, and solving the resulting equations. The process includes identifying when the function equals zero, factoring out common terms, and solving for x using algebraic methods. The tutorial concludes with the possible values for the zeros of the function.

What is the primary goal when finding the zeros of a function?

• To find when the function is at its minimum

• To find when the function equals zero

• To find when the function is at its maximum

• To find when the function is undefined

What substitution is made for f(x) in the initial setup?

• f(x) = 1

• f(x) = 0

• f(x) = x

• f(x) = z

Why is it challenging to isolate the variable in the given equation?

• Because the equation is quadratic

• Because the equation has different powers of x

• Because the equation is linear

• Because the equation is already solved

What common term is factored out to simplify the equation?

• 9

• x^4

• 25

• x^2

What equation is set up after factoring out common terms?

• x^2 = 0 or 9x^2 + 25 = 25

• x^2 = 0 or 9x^2 - 25 = 0

• x^2 = 0 or 9x^2 + 25 = 0

• x^2 = 0 or 9x^2 = 25

What is the next step after setting up the equation 9x^2 - 25 = 0?

• Subtract 25 from both sides

• Divide both sides by 9

• Multiply both sides by 9

• Add 25 to both sides

What should be considered when taking the square root of both sides?

• Both positive and negative roots

• Only the negative root

• Only the positive root

• No roots

What are the final possible values for the zeros of the function?

• 0, 5/3, -5/3

• 0, 3/5, -3/5

• 0, 5, -5

• 0, 3, -3