Question

Let a and b be real numbers such that x4+2x3−x2+ax+b=(Q(x))2 for some polynomial Q(x). What is the value of a + b?

Answer 1

Answer:

Step-by-step explanation:

x^-4 =0 => x=+/-2.

f(x)=ax^4+2x^3–3x^2+bx

f(2)=16a+16–12+2b=0

or 8a+b= -2…………(1)

f(-2)=16a-16–12–2b=0

8a-b=14…………..(2)

On adding eq.(1) & (2)

16a =12 => a = 12/16 = 3/4

Put a = 3/4 in eq. (1)

6+b=-2 =>b = -8

a =3/4 , b = -8 , Answer