If the equation `x^(2) - 3x + b = 0` and `x^(3) - 4x^(2) + qx = 0`, where `b ne 0, q ne 0` have one common root and the second equation has two equal roots, then find the value of `(q + b)`.

Answer

6

Explanation

`x^(2) - 3x + b = 0` ……(1)
Let the roots are `alpha + beta`.
`x^(3) - 4x^(2) + qx + 0`……(2)
One root of the equation is zero and other root is repeated
then roots are `0, beta, beta`, then
Sum of roots `2beta = 4`
`:. beta = 2`
`alpha + beta = 3` by equation `(1)`
`:. alpha = 1`
`:. b = alphabeta = 2`
`q = 0beta + beta^(2) + beta0 = beta^(2) = 4`
`:. (b + q) = (2 + 4) = 6`