One of the roots of equation x^(2)-(3p-4)x+11p-5=0 is 8. Find the other root. Find the value of p.

Other root is 9 and p = 7.

Step-by-step 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.