Find the quadratic equation whose roots are \(\frac{2}{3}\) and – 1

Explanation

The roots are \(\frac{2}{3}\) and - 1

Using x\(^2\) - (α + β)x +  αβ = 0

α + β =  \(\frac{2}{3}\) + (-1) =  \(\frac{2}{3}\) - 1 =  \(\frac{-1}{3}\)

αβ = \(\frac{2}{3}\) x (-1) = \(\frac{-2}{3}\)

x\(^2\) - (\(\frac{-1}{3}\) )x +  (\(\frac{-2}{3}\)) = 0

multiply through by 3

3x\(^2\) + x - 2 = 0