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If a and b are zeroes of the polynomial x2 – x – 6, then find a quadratic polynomial whose zeroes are (3a + 2b) and (2a + 3b).

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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

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