Question

1) If (x-4)is a factor of x^3+ax^2+2bx-24 and a-b=8, find the value a and b.

Answer 1

x- 4 is a factor

so, x =4 is a solution. Substitute it in the equation

x^3+ax^2+2bx-24 = 0
64+16a+8b-24 = 0
16a+8b+40 = 0

4a+2b = -10
Given a - b = 8

Solving,  4a+2b = -10
                2a-2b = 16
6a = 6
a = 1  and b = -7

Answer 2

HELLO DEAR,

given that:-

a - b = 8-------(1)


(x - 4)

=> x = 4 put in Equation

We get,

x³ + ax² + 2bx - 24

=> (4)³ + a(4)² + 2×b×4 - 24

=> 64 + 16a + 8b - 24 = 0

=> 8 + 2a + b - 3 = 0

=> 2a + b + 5 = 0

=> 2a + b = -5----(2)

from----(1) and---(2)

we get,

a - b = 8
2a + b = -5
——————
3a = 3

=> a = 1 put in--(1)

we get,

1 - b = 8

=> b = 1 - 8

=> b = -7 , a = 1

I HOPE ITS HELP YOU DEAR,
THANKS