Question

If (x-2) and (x-3) are the factors of x4+ax3+bx2+2x-24=0 the what is the answers

Answer 1

Step-by-step explanation:

$p(x) = {x}^{4} + a {x}^{3} + b {x}^{2} + 2x - 24$

g(x)=x-2

=>x=2

$p(2) = {2}^{4} + a ({2}^{3}) + b( {x}^{2} ) + 2(2) - 24$

=>16+8a+4b+4-24=0

=>8a+4b=4

=>2a+b=1

=>b=1-2a

f(x)=x-3

=>x=3

$p(3) = {3}^{4} + a( {3}^{3} ) + b( {3}^{2} ) + 2(3) - 24$

=>81+27a+9b+6-24=0

=>27a+9b=-63

=>3a+b=-21

=>b=-21-3a

b=b

1-2a=-21-3a

=>-a=22

=>a=-22