Find the value of a in the attachment
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Hey there!
From remainder theorem,
z - 3 = 0
z = 3.
f(z) = f(3).
g(z) = f(3).
Now,
f(z) = az³ + 4z² + 3z - 4
f(3) = a(3)³ + 4(3)² + 3 * 3 - 4
= 27a + 4 * 9 + 9 - 4
= 27a + 45 - 4
f(3) = 27a + 41
And,
g(z) = z³ - 4z + a
g(3) = (3)³ - 4 *3 + a
= 27 - 12 + a
g(3) = 15 + a
Now,
According to question,
f(3) = g(3)
27a + 41 = 15 + a
27a - a = 15 - 41
26a = - 26
a = - 26 / 26
a = - 1
Hope It Helps You!
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