Question

Find the value of ‘p’ for which the polynomial 2x^4 + 3x^3 + 2px^2 +3x + 6 is exactly
divisible by (x+2)...


answer in attachment.

help

thanks for help​

Answer 1

Step-by-step explanation:

Aloha !

f(p) = 2x⁴+3x³+2px²+3x+6

Given eqn is in A.P

Let p-d , p , p+d be the roots of eqn.

So, Sum of roots = p-d+p+p+d

Now,

p³= - 3

p= (-3)¹/³

p = -1

Solve with synthetic division.,

-1 || 2 3 -2 3 6

|| 0. -2. -1. 3 -6

_______________

2. 1 -3. 6 || 0

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Hope it helps you ✌️