8. If the polynomials az +42? + 32 - 4 and 2 - 43 + a leave the same remainder when divided by - 3. find the value of a
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Here, p(z)=a(z)
3 +4(z) 2 +3z−4, q(z)=(z) 3 −4z+a, and the zero of z−3 is 3.
So, by the given condition
p(3)=q(3)
a(3) 3 +4(3) 2 +3(3)−4=(3) 3 −4(3)+a
27a+4×9+9−4=27−12+a
27a+36+9−4=27−12+a
27a+45−4=15+a
27a+41=15+a
27a−a=15−41
26a=−26
a= 26−26
a=−1
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