Question

7. Value of p for which (x²+3x+2p) divisible by (x-2) is
(a)10
(b)-10
(c)5
(d)-5​

Answer 1

Answer:

(x-2)=0

x=2

(x²+3x+2p)=0

(2²+3*2+2p)=0

4+6+2p=0

10+2p=0

2p= -10

p= -5

Answer 2

Given,

• (x²+3x+2p) divisible by (x-2)

To Find,

• Value of p.

Solution,

p(x) = x²+3x+2p

p(x) = x²+3x+2pg(x) = x-2

p(x) is divisible by g(x) •••(Given)

g(x) = x-2

$\implies g(x) = x - 2 \\ \\\implies 0 = x - 2 \\ \\ \implies \boxed{x = 2}$

p(x) = x²+3x+2p

$\implies p(x) = {x}^{2} + 3x + 2p \\ \\ \implies p(2) = {(2)}^{2} + 3(2) + 2p \\ \\ \implies 0 = 4 + 6 + 2p \\ \\ \implies0 = 10 + 2p \\ \\ \implies - 10 = 2p \\ \\ \implies p = \frac{ - 10}{2} \\ \\ \implies \boxed{ p = - 5}$

Required Answer,

(d) -5