Question

plz answer fast its urgent need for exam

Answer 1

$Here \: is \: the \: answer \: of \: your \: question$


`$\textbf{We have to find a and b}$`

Now, according to question we have given,

x + 2 = 0

x = - 2

p(x) = ax³ + bx² + x - 2

Put the value of the x in above equation

p(-2) = a (-2)³ + b (-2)² - 2 - 2 = 0

- 8a + 4b - 4 = 0

- 2a + b - 1 = 0 ............(1)

In question it is also said that when p(x) is divided by (x - 2) then it leaves out remainder 4

Now value of x = 2 [As x - 2 = 0]

p(2) = a(2)³ + b(2)² + 2 - 2 = 0

= 8a + 4b = 0

= 2a + b = 0 ............(2)

Solve both (1) and (2) by elimination method,

- 2a + b = 1
+ 2a + b = 0
__________
0 + 2b = 1
___________

b = 1/2

Put value of b in (2)

2a + 1/2 = 0

2a = - 1/2

a = - 1/4