Math, asked by apkop33, 6 days ago

The polynomial ax^3+bx^2+x-6 has (x+2) as a factor and leaves a remainder 4 when divided by (x-2) .Find a and b

Answers

Answered by devanshu1234321

4

The polynomial ax³+bx²+x-6 has (x+2) as a factor and leaves a remainder 4 when divided by (x-2) .Find a and b

Let :-

p(x)=ax³+bx²+x-6

Using remainder theorem ,

x+2=0

x=-2

Since p(-2)=0

→p(-2)=a(-2)³+b(-2)²+x-6

→p(-2)=-8+4b-8

[p(-2)=0]

→-2a+b=2 (i)

Also when p(x) is divided by(x-2) remainder is o

→x-2=0

→x=2

→p(2)=4

→p(2)=a(2)³+b(2)²+(2)-6

→p(2)=8a+4b-4

→8a+4b=8

→2a+b=2 (ii)

(i)+(ii)

→(-2a+b)+(2a+b)=2+2

→2b=4

→b=2

put b=2 in (i)

→-2a+2=2

→-2a=0

→a=0

Thus,

a=0 and b=2

Answered by pushpr351

0

Answer:

Question :- If ax3 + bx2 + x – 6 has x + 2 as a factor and leaves a remainder 4 when divided by (x – 2), find the values of a and b.

Answer :- Solving (i) and (ii), we get a = 0 and b = 2 .

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