If a & b are the zeros of the polynomial x2 - x - 6.
X2 - (a+b)x + ab
So, x2 - x - 6 = x2 - (a+b)x + ab
On comparing, we get:
a + b = 1 ......(i) and
ab = -6 ........(ii)
The polynomial whose zeroes are (3a+2b) & (2a+3b) will be written as:
x2 - [(3a+2b) + (2a+3b)]x + [(3a+2b) x (2a+3b)]
= x2 - [3a+2b+2a+3b]x + 0 [from (iii)]
= x2 - [5a+5b]x + 0
= x2 - (5 x 1)x
= x2 - 5x