Question

If (x+2) is a factor of xsquare +ax+2b and a+b=4 then value of a and b

Answer 1

if x+2 is a factor , x= -2
substitute in the equation x square +ax+2b
= -2^2 + a ×-2 + 2×b = 0 (since x+2 is a factor p(x) =0

= 4-2a+2b =0 be equation 1
also given a+b =4
= b = 4-a be equation 2
substitute equation 2 in 1
= 4-2a+2(4-a)=0
= 4-2a+8-2a =0
= 12-4a = 0
= 12 = 4a
= a=3
since given a+b=4, we got a=3 then b=1

Answer 2

HEY MATE HERE IS YOUR ANSWER
$p(x) = {x}^{2} + ax + 2b$
x+2=0
x=-2

$p( - 2) = {-2}^{2} +a(-2) + 2b \\ 4 - 2a + 2b = 0 \\ - 2(a - b) = - 4 \\ a - b = 2 - - - - - > (2)$
but we know that a+b=4----(1)

eq(1)+eq (2)

a+b+a-b=4+2
2a=6
a=3----(3)

sub eq (3) in eq (1)
a+b=4
3+b=4
b=1

HOPE IT HELPS YOU

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