Question

If α, β are the roots of the equation 3y² + 4y + 1 = 0, form a quadratic equation whose roots are α², β².

Answer 1

The roots of the given equation are: -1/3 and -1

the roots squared are: 1/9 and 1

the quadratic equation whose roots are these is: (x - 1/9)(x - 1) = 0

Or: x² -^10x/₉ + ¹/₉ = 0

Answer 2

3y² + 4y + 1 = 0

3y² + 3y + y + 1 = 0

3y(y + 1) + 1(y + 1) = 0

(y + 1) + (3y + 1) = 0

y + 1 = 0

y(α) = -1

y(α²) = 1

or 3y + 1 = 0

y(β) = \(-\frac13\) 

y(β²) = \(\frac 19\)