Question

If 1 − 1 are two zeroes of the polynomial x^3+2x^2+ ax+b , then find the values of ​a and b

Answer 1

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 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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