The Equation 3x–1 + 5x–1 = 34 Has

Let α, β be the roots of the equation x² – ax + b = 0 and A_n = αⁿ + βⁿ. 

Let f (x) = ax² + bx + c, a, b, c Ïµ R. if f (x) takes real values for real values of x and non – real values for non – real values of x, then.

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

The condition that the equation  has real roots that are the equal in magnitude but opposite in sign is

If x is real, and 

Let a > 0, b > 0 and c > 0. Then both the roots of the equation ax² + bx +c = 0

Let a, b, c be non – zero real number such that

Then the quadratic equation ax² + bx + c = 0 has

If the harmonic mean between roots of   is 4 then b equals