Quadratic Equations

If α ≠ β but α2 = 5α - 3 and β2 = 5β - 3, then the equation having α/β and β/α as its roots is

  1. 3x2 - 19x - 3 = 0
  2. 3x2 - 19x + 3 = 0
  3. x2 - 5x + 3 = 0
  4. 3x2 + 19x - 3 = 0

Solution

The equation having α and β as its root will be:

x2 - (α+β)x + αβ = 0 and since α2 = 5α-3 and β2 = 5β-3 shows that α and β are roots of equation

x2 - 5x + 3 = 0 this implies α+β = 5 and αβ = 3

You can use these relations to calculate the equation having α/β and β/α as its root. 

(α/β)*(β/α) = 1 and  β/α + α/β = 19/3

Therefore, the equation is 3x2 - 19x + 3 = 0

The correct option is B.