Question

find the value of A and B so that x^2 - 4 is a factor of ax^4 + 2x^3 - 3x^2 + bx - 4
plz answer properly
and step by step​

Answer 1

Answer:

a = 1, b = 8

Step-by-step explanation:

f(x) = ax^4+2x^3–3x^2-bx-4

x^2 - 4 = (x-2) (x+2) are factors of f(x).

x-2=0 =>x=2

f(2)=16a+16–12–2b-4=0

16a-2b=0, or 8a - b =0………….(1)

x+2=0 => x=-2

f(-2)=16a-16–12+2b-4=0

16a+2b=32 , or 8a+b =16…………..(2)

On adding eq. (1) & (2)

16a=16 , a =16/16=1.

put a =1 in eq.(1)

8×1 -b =0 , or b=8.

a = 1 , b = 8 ,

Hope it helps!

Answer 2

Answer:

a=1 , b=-8

Step-by-step explanation:

x²-4 is a factor

so the roots of x²-4 are also the roots of the given polynomial

x²-4=0

x²=4

x=±2 sub in given polynomial

Sub x=2

16a+16-12+2b-4=0

16a+2b=0

8a+b=0.................(1)

sub x=-2 in given polynomial

16a-16-12-2b-4=0

16a-2b-32=0

8a-b=16....................(2)

(1)-(2)

2b=-16

b=-8 sub in (1)

8a-8=0

8a=8

a=1

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