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Directions : Read the following information carefully and answer the question given below. Equation 1: x 2 - 8x + c = 0 Equation 2: y 2 - 5y + c - 9 = 0 Roots of the equation 1 are: a and b, and roots of the equation 2 are: a and (b - a).

If we multiply equation 2 by 2^t and add 3 to the largest root of the equation newly formed, then find the number thus formed.

From the first equation x^2 - 8x + c = 0, the sum of the roots is a + b = 8. For the second equation y^2 - 5y + c - 9 = 0, the sum of its roots is a + (b - a) = b = 5. Substituting b = 5 into the first sum gives a = 3, and using the product of roots in the first equation gives c = 15. The roots of the second equation are 3 and 2, making the largest root 3. Multiplying equation 2 by 2 gives 2y^2 - 10y + 12 = 0, which has identical roots of 3 and 2, so the largest root remains 3. Adding 3 to this largest root results in 6.

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