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: 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

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)

answer: sorry but i need points

step-by-step explanation:

answer:  

step-by-step explanation:

here x represents the height of the pole,

and, the height of the shadow of the pole is 12 feet.

also, the angle of elevation from the top of the pole is 40°,

therefore,

by the low of sine,

which is the required equation for finding the value of x,