Question help (1 Viewer)

[Dashdorm24]

The polynomial P(x) = x^2 + ax + b has a zero at x=2. When P(x) is divided by x+1, the remainder is 18. Find the value of a and b.

Would appreciate all help, thanks

 

[CM_Tutor]

If has a zero at then must be a factor of . We know that is monic (coefficient of is 1) and so it can be factorised as for some constant .

Now, when is divided by , the remainder is 18, meaning that



So, our polynomial is



and so and

 

[davidgoes4wce]

The polynomial P(x) = x^2 + ax + b has a zero at x=2. When P(x) is divided by x+1, the remainder is 18. Find the value of a and b.

Would appreciate all help, thanks

I had a slightly different way of doing it

P(-1)=18
P(2)=0

18=(-1)^2+a(-1)+b
18=1-a+b
17=-a+b equation A

0=2^2+2a+b
-4=2a+b equation B


subtract equation A -B

21=-3a
a=-7

sub a=-7, 17=-(-7)+b
b=24

 

[CM_Tutor]

I had a slightly different way of doing it

P(-1)=18
P(2)=0

18=(-1)^2+a(-1)+b
18=1-a+b
17=-a+b equation A

0=2^2+2a+b
-4=2a+b equation B


subtract equation A -B

21=-3a
a=-7

sub a=-7, 17=-(-7)+b
b=24

Yes, this is the more obvious way... my approach was more suited to the question where P(x) is a polynomial of degree .

But, there is an error in the last step of your calculation. It should say: