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Chapter 1: Problem 174

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

Short Answer

Expert verified
The quadratic equation with the solution set {-3,5} is \(x^2 -2x -15 =0\)

Step by step solution

01

Identify and list the roots of the equation

The given roots of the quadratic equation are -3 and 5.
02

Use the formula for the sum of roots

The sum of the roots is equal to -b/a. This would be equal to the sum of -3 and 5, or 2. Since a is typically set to 1 in a standard quadratic equation, -b would therefore be 2, and b is -2.
03

Use the formula for the product of roots

The product of the roots is equal to c/a. Thus, multiplying -3 and 5 gives -15 which would be equal to c/a. Considering a to be 1 (as is typical), c would therefore be -15.
04

Formulate the quadratic equation

Having obtained a, b, and c as 1, -2, and -15 respectively, plug these values into the standard form of a quadratic equation to get the required equation. The equation would be \(x^2 -2x -15 =0\)

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