# If the polynomial az3+4z2+3z-4 and z3-4z+a leaves the same remainder when divided z-3.find a

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by uganesh2005

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by uganesh2005

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zero of the polynomial (z-3) = 3

(since,z-3=0⇒z=3)

So,replacing z by 3,

f(3) = a(3)³+4(3)²+3(3)-4

⇒f(3) = 27a+36+9-4

⇒f(3) = 27a+41

Let g(z) = z³-4z+a

zero of the polynomial (z-3) = 3

(since,z-3=0⇒z=3)

So,replacing z by 3,

g(3) = (3)³-4(3)+a

⇒g(3) = 27-12+a

⇒g(3) = 15+a

Given that the two polynomials leaves same remainder when divided by z-3

So,g(3)=f(3)

⇒15+a = 27a+41

⇒15-41 = 27a - a

⇒-26 = 26a

⇒a = -1.