Question

The expression 2x4-5x2+ax+b has a
factor(x+2) and leaves remainder of 6 when divided b x-1 Calculate
the value of a and b.

Answer 1

The expression 2x⁴-5x²+ax+b has a factor (x+2)

x+2=0
⇒x=-2

Put x=-2 in given expression,

2(-2)⁴-5(-2)²+a(-2)+b=0

2(16)-5(4)-2a+b=0

32-20-2a+b=0

12-2a+b=0

-2a+b=-12--------(1)

The expression leaves remainder 6 when divided by x+1

x+1=0
⇒x=-1

2(-1)⁴-5(-1)²+a(-1)+b=6

2(1)-5(1)-a+b=6

2-5-a+b=6

-a+b=6-2+5

-a+b=9------(2)

(1)-(2)

-2a+b-(-a+b)=-12-9

-2a+b+a-b=-21

-a=-21

a=21

Put a=21 in (2)

-a+b=9

-21+b=9

b=30

Therefore,a=21 and b=30

Hope it helps