Question

If x-1 and x-2 are factors of polynomial x^3-px^2+qx-6,then find the value of p and q

Answer 1

Answer:

Step-by-step explanation:  x³ - px² + qx - 6

                                             x-1

                                             x = 1

1³ - p(1)² + q(1) - 6 = 0

1 -p +q -6 = 0

-p +q -6 +1 = 0

-p + q -5 = 0

p - q = -5 ---------- (i)

x-2

x=2

2³ - p(2)² + q(2) - 6 = 0

8 - 4p + 2q - 6 = 0

-4p +2q - 6 + 8 = 0

-4p + 2q + 2 = 0

4p -2q = 2 ---------- (ii)

p - q = -5 x4

4p -2q = 2 x1

4p -4q = -20 ----------- (iii)

4p - 2q =2 ------------ (iv)

Subtract equ iv from equ iii

-2q = -22

q = 11

p - q = -5

p - 11 = -5

p = -5 + 11

p = 6