Question

Find the value of a and b so that x+1 and x+2 are the factors of x⁴+ax³+2x²-3x+b.

Answer 1

zeroes are -1&-2
sum of zeroes=-coefficent of x2/coefficient of x3

-2-3=a
-5=a

product of zeroes=constant term/coefficient of x4

-2*-3=b
6=b

Answer 2

Answer:

The key technique here is to be able to use remainder theorem.

Let me define p(x) as $x^4+ax^3+2x^2-3x+b$

According to the remainder theorem:

p(-1)=0 and p(-2) =0

Also,

$p(-1)=(-1)^4+a(-1)^3+2(-1)^2-3(-1)+b=1-a+2+3+b=-a+b+6$

$p(-2)=(-2)^4+a(-2)^3+2(-2)^2-3(-2)+b=16-8a+8+6+b=-8a+b+30$

∴$-a+b+6=0$ (1)

$-8a+b+30=0$ (2)

Solving (1) and (2) simultaneously yields the following results:

a=24/7 , b=-18/7

Hope it helps :)

Step-by-step explanation: