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Answers
Answer:
a = 1, when R1 = R2. a = -2.354 when R1 + R2 = 0. a = 0.1417, when 2R1 - R2 = 0.
Step-by-step explanation:
f(x) = a + 3 - 3
f(x) when divided by (x - 4) leaves remainder
i.e. when f(x) - is divided by (x -4), remainder will be zero.
⇒ (x-4) = 0, is a factor of f(x) -
⇒ x = 4, is a factor of f(x) -
f(x) - = 0, for x = 4
a + 3 - 3 - = 0, for x = 4
⇒ a × + 3 × - 3 - = 0
64a + 3 × 16 - 3 - = 0
= 64a + 48 - 3 = 64a + 45
similarly,
g(x) - = 0, for x = 4
2 - 5 + a - = 0, for x = 4
2 × - 5 × 4 + a - = 0 = 0
2 × 64 - 20 + a - = 0
= 128 - 20 + a = 108 + a
when = ,
64a + 45 = 108 + a
64a - a = 108 - 45
63a = 63, ⇒ a = 1
when + = 0,
(i.e. when = - )
64a + 45 = -(108 + a)
64a + 45 = -108 - a
64a + a = -108 -45
65a = -(108 + 45)
65a = -153
a =
a = - ( )
a = - ( )
a = - 2.354
(153 when divided by 65 leaves a remainder 23, quotient = 2)
(answer = quotient + (remainder/divisor), 153 = 2 + (23/65)
when - = 0,
(i.e. = )
108 + a = 2 × (64a + 45)
108 + a = 2 × 64a + 2 × 45
108 + a = 128a + 90
128a - a = 108 - 90
127a = 18
a = ≅ 0.1417