Question

If α and β are the roots of the quadratic polynomial 6y 2 -7y+2, Find a quadratic polynomial whose zeroes are1/ α and 1/ β .

Answer 1

6y²-7y+2            [by middle term splitting]
6y²-4y-3y+2
2y(3y-2)-1(3y-2)
(3y-2)(2y-1)
   α        β
α=2/3    β=1/2
1/α=3/2
1/β=2
1/α+1/β=3/2+2
               7/2
1/α×1/β=3/2×2
                3

polynomial= x²-(1/α+1/β)x+1/α×1/β
                    x²-7/2x+3
multiply by 2
2x²-7x+6