Question

If α and β are the roots of the quadratic equation x^2 + x - 14
then what is the value of α^4 + β^4 ??????????

Answer 1

x²+x+14.

sum of roots = -1=α+β
product= -14= αβ

α⁴+β⁴= (α²+β²)²-2(αβ)² = ((α+β)²-2αβ)²-2(αβ)²)

=((-1)²-2(-14))² -2(-14)²)= 841+784=1625