if x^3+2x^2+ax+b has factors x+1 and x-1 then find a and b
Answers
Question :
if x³ + 2x² + ax + b has factors (x+1) and (x-1) then find a and b
Answer :
- a = -1
- b = -2
Given :
- polynomial, x³ + 2x² + ax + b
- factors : (x+1) and (x-1)
To find :
values of a and b
Solution :
Given polynomial,
x³ + 2x² + ax + b
⟹ (x+1) is a factor
x + 1 = 0
x = -1
Since (x+1) is a factor,
when we substitute the value of x = -1, we get 0.
⇒ x³ + 2x² + ax + b
⇒ (-1)³ + 2(-1)² + a(-1) + b = 0
⇒ -1 + 2(1) - a + b = 0
⇒ -1 + 2 - a + b = 0
⇒ b - a + 1 = 0
⇒ a - b = 1 ---- (1)
⟹ (x-1) is a factor
x - 1 = 0
x = 1
Since (x-1) is a factor,
when we substitute the value of x = 1,we get 0
⇒ x³ + 2x² + ax + b
⇒ (1)³ + 2(1)² + a(1) + b = 0
⇒ 1 + 2(1) + a + b = 0
⇒ 1 + 2 + a + b = 0
⇒ a + b + 3 = 0
⇒ a + b = -3 ---- (2)
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ADDING BOTH EQUATIONS,
a - b = 1
a + b = -3
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2a = -2
a = -2/2
a = -1
Substitute the value of a in any equation,
a - b = 1
-1 - b = 1
b = -1 -1
b = -2
║ a = -1 and b = -2
Answer:
a= -1 and b= -2
Step-by-step explanation:
show the photo that is given up
