Find the value of `a` for which one root of the quadratic equation `(a^2-5a+3)x^2+(3a-1)x+2=0` is twice as large as the other.

Explanation

Let the roots be `alpha and 2alpha` Then,
`alpha + 2alpha = (1-3a)/(alpha^(2) -5a + 3),alpha xx2alpha = (2)/(alpha^(2) - 5a + 3)`
or ` 2[(1)/(9) ((1-3a)^(2))/((alpha^(2) -5a + 3)^(2))] = (2)/(alpha^(2) - 5a + 3)`
or `((1 - 3a)^(2))/(alpha^(2) - 5a + 3) = 9 or 9alpha^(2) - 6a + 1 = 9^(2) - 45a + 27`
or `39a = 26 or a = (2)/(3)`