Question

polynomials answerif X square + 2 X square + a x + b has factor X + 1 and x minus 1 then find a and b ​

Answer 1

Answer:

your answer is in above attachment...!!

Answer 2

Given :-

x + 1 and x - 1 are the factors of polynomial x² + 2x² + ax + b = 3x² + ax + b

here, we've to find the value of a and b

when x = -1 (x + 1 as factor),

➡ p(-1) = 3(-1)² + a(-1) + b = 0

➡ -3 - a + b = 0

➡ -a + b - 3 = 0 -------(i)

when x = 1(x - 1 as factor),

➡ p(1) = 3(1)² + a(1) + b = 0

➡ 3 + a + b = 0

➡ a + b + 3 = 0 -------(ii)

subtracting equation (ii) from (i), we get

➡ (-a + b -3) - (a + b + 3) = 0

➡ -a + b - 3 - a - b - 3 = 0

➡ -2a - 6 = 0

➡ -2a = 6

➡ a = 6/-2

➡ a = -3

substituting a = -3 in equation (i),

➡ -(-3) + b - 3 = 0

➡ 3 + b = 3

➡ b = 3 - 3

➡ b = 0

hence, the value of a = -3 and b = 0