Equations and I...

If α and β are the roots of χ² - 2χ + 4 = 0, then thevalue of α⁶ + β⁶ is

If α ,β and γ are the roots of χ³ + 4χ + 1 = 0, then the equation, whose roots are

The number of real solutions of the equation | x |² – 3 | x | + 2 = 0 is

If α ,β and γ are such that α + β + γ = 2, α² + β² + γ² = 6, α³ + β³ + γ³ = 8 then α⁴ + β⁴ + γ⁴ is equal to

Let the two numbers have arithmetic mean 9 and geometric mean 4. Then, these numbers are the roots of the quadratic equation

If α and β are the roots of the equations χ² - (1 + n² )χ+ 1/2(1 + n² + n⁴) = 0, then α² + β² is equal to

If α and β are the roots of χ² - 2χ cos ∅ + 1 = 0, then the equation, whose roots are αⁿ + βⁿ

If α, β and γ are the roots of the equation χ³ - 8 χ + 8 = 0, then ∑a² and ∑ 1/αβ are respectively

If α and β are the roots of the equation aχ² + bχ + c = 0, αβ = 3, and a, b, c are in AP, then α + β is equal to

If α and β are the roots of the equation χ² + aχ + b = 0, then