Question

Plz solve it guys plz

Answer 1

Answer :D

1). for x:

x - 1 = 0

x = 1

for k:

2(1)³ + 9(1)² + 1 + k = 0

2 + 9 + 1 + k = 0

k + 12 = 0

k = -12

2). x - 4 = 0 <=> x = 4

now,

putting this value in 2x³ - 3x² - 18x + a

we have

2(4)³ - 3(4)² - 18(4) + a = 0

2 × 64 - 3 × 16 - 18 × 4 + a = 0

128 - 48 - 72 + a = 0

128 - 120 + a = 0

a = -8

3). Let f(x) = ax³ + x² - 2x + 4a - 9

Given (x + 1) is a factor of  f(x), so f(-1) = 0

f(x) = ax³ + x² - 2x + 4a - 9

f(- 1) = a( - 1 )³ + (- 1 )² - 2  (- 1) + 4a - 9

0 = - 1a + 1 + 2 + 4a - 9

0 = - 1a + 4a + 1 + 2 - 9

0 = 3a + 3 - 9

0 = 3a - 6

-3a = - 6

a = 6/3

a = 2

4). given ,

f(x)=x⁴-x³-11x²-x+a

g(x)=x+3

compairing x+3 with x-a 

a=-3

 now , for the f(x) to be exactly divisible by x+3

f(a)=0

or,(-3)⁴-(-3)³-11*(-3)²-(-3)+a =0

or,81-27-99+3+a=0

or,-42+a=0

or,a=42

so the required value of a is 42.

5). In the attachment ☺️