If a polynomial P(x) is divisible by x - a, P(a) = 0.

The polynomial P(x) = ax^2 + bx + 4 is divisible by x - 2 and x - 1.

This gives: P(2) = 0 and P(1) = 0

P(2) = 0

=> a*4 + b*2 + 4 = 0

P(1) = 0

=> a + b + 4 = 0

a + b + 4 = 0

=> a = -4 - b

Substitute in a*4 + b*2 + 4 = 0

=> (-4 - b)*4 + 2b + 4 = 0

=> -16 - 4b + 2b + 4 = 0

=> -2b = 12

=> b = -6

a = 2

**The value of a = 2 and b = -6; the polynomial P(x) = 2x^2 - 6x + 4**

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