Answer:
Other root is 9 and p = 7.
Explanation:
x^(2) - (3p-4)x + 11p-5 = 0 , x = 8.
Let the other root be A, then using the formula for the product and sum of the roots of a quadratic equation:
8* A = 11p - 5
8 + A = -(-(3p - 4))
8 + A = -(-3p + 4)
8 + A = 3p - 4
A = 3p - 12.
Multiply this last equation by 8:
8A = 24p - 96
Now subtract the first equation from this:
8A - 8A = 24p - 11p - 96- (-5)
0 = 13p - 91
13p - 91 = 0
p = 91/13 = 7
and A = 3(7) - 12
= 9.