Question

x + 3 is a factor of x3 + ax2 -bx + 6 and a + b = 7 , find the value of a and b.

Answer 1

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Answer 2

Answer:

a = 0, b = 7

Step-by-step explanation:

if (x+3) is a factor that means that x = -3

therefore x^3 + ax^2 - bx + 6 = 0 =>

(-3)^3 + (-3)^2a - (-3)b + 6 = 0 =>

-27 + 9a + 3b + 6 = 0 =>

9a + 3b = 21 - statement 1

a + b = 7 - statement 2

multiply statement 1 by 1 and statement 2 by 3

9a + 3b = 21

3a + 3b = 21

from statement 1 and 2 we get

9a + 3b - 3a - 3b = 21 - 21

6a = 0

substitute the value of a in statement 1

0 + b = 7 =>

b = 7