Question

If f(x) = x4 + ax3 + bx2 + cx + d is a polynomial such that f(1) = 5, f(2) = 10, f(3) = 15, f(4) = 20, then the value of f(5) + f(–5) is

Answer 1

Answer:

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Step-by-step explanation:

1)=10f(1)−10=0

f(2)=20⇒f(2)−20=0⇒f(2)−10×2=0

f(3)=30⇒f(3)−30=0⇒f(3)−10×3=0

g(a)=f(x)−10x=0

∴g(1)=f(1)−10=0

g(2)=f(2)−20=0

g(3)=f(3)−30=0

∴g(1)=g(2)=g(3)=0

⇒(x−1)(x−2)(x−3)dividesg(x)

g(x)=f(x)−10x=(x−t)(x−1)(x−2)(x−3)

f(x)=10x(x−t)(x−1)(x−2)(x−3)