Problem 174 - Algebra and Trigonometry

Question

Write a quadratic equation in general form whose solution set is \(\\{-3,5\\}\).

Step-by-Step Solution

Answer

Thus, the quadratic equation in general form with roots -3 and 5 is \(y = x^2 - 2x - 15\).

Step 1: Express the quadratic equation in factored form

The given roots are -3 and 5. So the quadratic equation can be written in the format of \(y = a(x - p)(x - q)\) where p and q are the roots and a is a nonzero constant. We substitute -3 for p, 5 for q and take a as 1 for simplicity to get: \(y = (x + 3)(x - 5)\)

Step 2: Expand the quadratic

Apply the distributive law \(a(b + c) = ab + ac\) to expand the equation to obtain \(y = x^2 - 5x + 3x - 15\)

Step 3: Simplify the equation

Collect like terms \(x^2 - 5x + 3x - 15\) to obtain \(y = x^2 - 2x - 15\).