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Answer:
other root: x = 9
p = 7
Step-by-step explanation:
first, find p:
(8)² - (3p - 4)8 + 11p -5 = 0
64 - (24p - 32) + 11p - 5 = 0 –––––> 64 - 24p + 32 + 11p - 5 = 0
91 - 13p = 0
-13p = -91
p = 7
plug in p to find the polynomial:
x² - (3(7) - 4)x + 11(7) - 5 = 0
x² - (21 - 4)x + 77 - 5 = 0
x² - 17x + 72
find the roots:
we know that 8 is one of the roots, so one factor is (x - 8)
the other number needs to be something that equals -17 when added with -8 and 72 when multiplied by -8
that number is -9
so the poly nomial factors to be: (x-8)(x-9)
so the roots are x = 8 and x = 9
Answer:
p = 7
Step-by-step explanation:
x²-(3p-4)x+11p-5=0 ...(1) Root: 8, x-8 is factor
(x-8) (x- (11p-5)/8) = 0
x² -8x - ((11p-5)/8)*x + (11p-5) = 0
x² - (8 + (11p-5)/8) x + 11p-5 = 0 ----(2)
compare(1) and (2): 3p-4 = 8 + (11p-5)/8
24p - 32 = 64 + 11p - 5
13p = 91
p = 7
check: x²-(3p-4)x+11p-5 = x²- 17x + 72 = (x-8)(x-9)