Question

If x2+ax+b,when divided by x-4,leaves remainder of 32 and x2+bx+a,when divided by x-4, leaves a remainder of 35, then a+b=?

Answer 1

when x^2+ax+b is divided with x-4
x-4=0
x=4
p(x)=x^2+ax+b=32
p(4)=4^2+a(4)+b=32
=16+4a+b=32
=4a+b=32-16
=4a+b=16 ____(1)

when x^2+bx+a is divided with x-4
p(x)=x^2+bx+a=35
p(4)=4^2+b(4)+a=35
=16+4b+a=35
=4b+a=35-16
=4b+a=19 _____(2)

4a+b=16
(+)a +4b=19
________
5a+5b=35
________
5a+5b=35
a+b=35/5+5
a+b=12

$hope \: it \: helps$