If 1 − 1 are two zeroes of the polynomial x^3+2x^2+ ax+b , then find the values of a and b
Answers
Answer:
f(1) = x^3+2x^2+ ax+b
= 1^3 +2.1^2 +1a +b =0
= 1 + 2 + a + b = 0
= a +b= -3 -------(i)
when f(-1) = x^3+2x^2+ ax+b
= -1^ 3 + 2(-1^2) -1a +b = 0
= -1 +2 -a+b =0
= -a +b = -1
= a-b = 1 --------(ii)
Adding equ (i) & (ii)
a+b=-3
a-b= 1
______
2a = -2
a = -1
Putting value of a in equation (i) . we get,
a+b=-3
-1 +b=-3
b = -2
Answer:
a = -1, b = -2
Step-by-step explanation:
Let f(x) = x³ + 2x² + ax + b
Given, 1, -1 are zeroes are f(x)
So, f(1) = 0 and f(-1) = 0
f(-1) = 0
⇒ (-1)³ + 2(-1)² + a(-1) + b = 0
⇒ -1 + 2 - a + b = 0
⇒ b = a - 1
f(1) = 0
⇒ 1³ + 2(1)² + a(1) + b = 0
⇒ 1 + 2 + a + a - 1 = 0
⇒ 3 + 2a - 1 = 0
⇒ 2a + 2 = 0
⇒ 2a = -2
⇒ a = -2/2 = -1
b = a - 1 = -1 - 1 = -2
∴ a = -1, b = -2
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