If -2 and 3 are zeroes of quadratic polynomial xsquare + (a+1)x+b then find the value of and b

a = - 2, b = - 6

Step-by-step explanation:

Substitute the values of the zeros into the polynomial and equate to zero.

x² +(a + 1)x + b

x = - 2 → (- 2)² - 2(a + 1) + b = 0 , that is

4 - 2a - 2 + b = 0

2 - 2a + b = 0 ( subtract 2 from both sides )

- 2a + b = - 2 → (1)

x = 3 → 3² + 3(a + 1) + b = 0, that is

9 + 3a + 3 + b = 0

12 + 3a + b = 0 ( subtract 12 from both sides )

3a + b = - 12 → (2)

Subtract (1) from (2) term by term to eliminate b

5a = - 10 ( divide both sides by 5 )

a = - 2

Substitute a = - 2 into either of the 2 equations and evaluate for b

Substituting into (2)

3(- 2) + b = - 12

- 6 + b = - 12 ( add 6 to both sides )

b = - 6

Thus a = - 2 and b = - 6

answer 1 : option "c"

answer 2 : option "d"

answer 3 : option "b"

answer 4 : option "d"

answer 5 : option "b"

answer 6 : option "a"

answer 7 : option "c"

answer 8 : option "d"

answer 9 : option "c"

answer 10 : option "d"

answer 11 : option "c"

answer 12 option "b"

answer 13 option "c"

answer 14 option "c"

answer 15 option "d"

answer 16 option "a"

answer 17 option "b"

answer 18 option "c"

answer 19 option "a"

answer 20 option "a"

answer 21 option "c"

d