Question

If(x-2) is factor of x power 3 +axpower 2 +bx +18 and a-b =7 find a and b

Answer 1

a value is -2

b value is -8

Answer 2

HEYA FRIEND HERE IS YOUR ANSWER

p(x)= x³ + ax² + bx + 18

(x-2) is the factor of p(x)

∵ x-2=0

    x=2

p(2)= (2)³ + a(2)² + b(2) + 18

     = 8 + 4a + 2b + 18

     = 26 + 4a + 2b

∵ p(2)=0

∴ 26 + 4a + 2b = 0            (1)

It is given that a-b=7

∴ a=7+b              (2)

Substituting the value of a in (1) we get

26 + 4(7+b) + 2b = 0

26 + 28 + 4b + 2b = 0

54 + 6b = 0

6b = -54

b = -54/6

b = -9

Substituting the value of b in (2) we get

a = 7-9

a = -2

HOPE IT HELPS YOU!!