. If x +1 and x -1 are factors of f(x) = x³ +2 ax +b, calculate the values of a and b. Using these values of a and b, factorise f(x) completely.
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Answers
Answer:
because x+1 x-1 is a factor then value of x = both 1 and -1
Step-by-step explanation:
f(1)=1 power 3 + 2
=F(1)=1+2 = 3 is first value and
f(-1) =-1 power 3 + 2
= -1 + 2 = f(-1)= 1
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Answer:
a = -1/2 and b = 0 , f(x) = x(x + 1)(x - 1)
Step-by-step explanation:
Using factor theorem:
If (x + 1) is a factor of f(x), f(-1) = 0
⇒ (-1)³ + 2a(-1) + b = 0
⇒ -1 - 2a + b = 0
⇒ b - 2a = 1 ...(1)
If (x - 1) is a factor f(x), f(1) = 0
⇒ (1)³ + 2a(1) + b = 0
⇒ 1 + 2a + b = 0
⇒ 2a + b = -1 ...(2)
Adding (1) and (2), we get b = 0
Substituting b in (1), 0 - 2a = 1 ⇒ a = -1/2
Therefore, f(x) = x³ + 2(-1/2)x + 0
= x³ - x
= x(x² - 1)
= x(x + 1)(x - 1)
*If f(x) = x² + 2ax + b, then following the same procedure:
a = 1/2 and b = 0
f(x) = x² - 1