Question

x^2 + bx + c has factors x-1 and x + 2 then b + c = ​

Answer 1

Answer:

3/2

Step-by-step explanation:

Since (x - 1) & (x + 2) are factors of f(x), the remainders will be equal to zero.

Case 1 :

x - 1 = 0

x = 1

Substituting the value of x in f(x), we get :

f(1) => $1^{2} + b.1 + c$ = 0

f(1) => 1 + b + c = 0

Case 2 :

x + 2 = 0

x = -2

Substituting the value of x in f(x), we get :

f(-2) => $2^{2} + b.2 + c$ = 0

f(-2) => 4 + 2b + c = 0

Comparing f(1) & f(-2), we get :

f(1) x 2 & f(-2) x 1

Subtracting f(1) & f(-2), we get :

2 + 2b + 2c = 0

(-)4 (-)2b (-)c = 0

→ -2 - c = 0

→ c = -2

Substituting the value of c in f(1), we get :

1 + 2b + (-2) = 0

1 + 2b - 2 = 0

2b - 1 = 0

b = 1/2

∴ b + c = 1/2 + (-2)

b + c = (1-4)/2

b + c = 3/2