Question

If f(x) is a polynomial such that f(x^2+1)=x^4+4x^2 and f(x^2−1)=ax^4+4bx^2+c,then a^2+b^2+c^2=?
plz give meaningful solution ​

Answer 1

Answer:

17

Step-by-step explanation:

f(x^2+1)=x4+4x^2 ...(1)

f(x^2–1)=ax^4+4bx^2+c ...(2)

Put x^2=y^2–2 in Eq. (1)

f(y^2–2+1)=(y^2–2)2+4(y^2–2)

f(y^2−1)=y4–4y^2+4+4y^2–8

f(y^2–1)=y^4–4

⟹f(x^2–1)=x^4–4 ...(3)

Compare (2) and (3)

a=1,b=0,c=−4

Hence a^2 + b^2 + c^2 = (1)^2 + (0)^2 + (-4)^2

Therefore the answer is 17