Question

If α and β are the roots of the quadratice equation x²- 2x - 7= 0, find the
value α² + β²

Answer 1

x²- 2x - 7= 0
Here, a = 1, b = -2, c = -7
`α + β = (−b)/a =(-(-2))/1 = 2`
`α β =c/a=(-7)/1 =7`
α² + β ² = (α + β)²-2 αβ
             =(2)² -2 × (-7)
             = 4 + 14
             = 18