Question

Using what you learned in this lesson, create an equation that has 53 and 22 as its only solutions.

Answer 1

Using the Factor Theorem, the equation is:

$f(x) = x^2 - 75x + 1166$

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The factor theorem states that an equation with solutions $x_1, x_2,...x_n$ is written as:

$f(x) = a(x - x_1)(x - x_2)...(x - x_n)$

In which a is the leading coefficient.

In this problem:

• Solutions of 53 and 22, thus $x_1 = 53, x_2 = 22$
• Choosing a leading coefficient of 1.

The equation is:

$f(x) = (x - 53)(x - 22)$

$f(x) = x^2 - 75x + 1166$

A similar problem is given at https://brainly.com/question/24380382