Question

α, β are roots of y² – 2y –7 = 0 find, 

α² + β² 

Answer 1

α, β are roots of y² – 2y – 7 = 0 

a = 1, b = -2, c = -7 

\[\alpha + \beta = \frac{- b}{a} = \frac{- \left( - 2 \right)}{1} = 2\]
\[\alpha\beta = \frac{c}{a} = \frac{- 7}{1} = - 7\] 

\[\alpha^2 + \beta^2 = \left( \alpha + \beta \right)^2 - 2\alpha\beta\]

\[ = \left( 2 \right)^2 - 2\left( - 7 \right)\]

\[ = 4 + 14\]

\[ = 18\]