Question

1) If x + ax² - 11x + b has (x-3) as a factor and leaves ramainder 32, when divided by (x+5),
find the value of a and b.​

Answer 1

Answer:

a = -3 and b = 57

Step-by-step explanation:

In polynomial x + ax² - 11x + b has (x-3) as a factor.

x - 3 = 0

x = 3

p(3) = 3 + a(3)² - 11(3) + b = 0

p(3) = 3 + 9a - 33 + b = 0

p(3) = 9a - 30 + b = 0

p(3) = 9a + b = 30 ...........(1)

Leave a remainder 32 when divided by (x + 5)

p(-5) = -5 + a(-5)² - 11(-5) + b = 32

p(-5) = -5 + 25a + 55 + b = 32

p(-5) = 25a + b + 50 = 32

p(-5) = 25a + b = -18 ...........(2)

Subtract (1) & (2) equation

→ 25a + b - 9a - b = -18 - 30

→ 16a = - 48

→ a = -3

Substitute value of a in (1)

→ 9(-3) + b = 30

→ -27 + b = 30

→ b = 57

Answer 2

Answer:

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