Question

Write the quadratic equation that has roots -1 2/3 and -1 + 2/3 , if it's coefficient with x² is equal to

a.) -3/5
b.) 3/3

Answer 1

The quadratic equation from the roots is f(x) = 3/5x² - 5/3

How to determine the quadratic equation from the roots

From the question, we have the following parameters that can be used in our computation:

Roots = -1 2/3 and 1 2/3

This means that

Roots = -5/3 and 5/3

So, we have the quadratic equation to be

f(x) = a(x + 5/3)(x - 5/3)

This gives

f(x) = a(x² - 25/9)

The coefficient is 3/5

So, we have

f(x) = 3/5(x² - 25/9)

Expand

f(x) = 3/5x² - 5/3

Hence, the quadratic equation from the roots is f(x) = 3/5x² - 5/3