Question

Find the value of p and q if the polynomial

Answer 1

Answer:

here is ur answer pls check dear

Step-by-step explanation:

(x^4 + px^3 + 2x^2 - 3x + q) / (x^2 - 1) = ax^2 + bx + c

ax^4 - ax^2 + bx^3 - bx + cx^2 - c = x^4 + px^3 + 2x^2 - 3x + q

ax^4 = x^4

a = 1

-ax^2 + cx^2 = 2x^2

-a + c = 2

-1 + c = 2

c = 3

-c = q

-3 = q

bx^3 - bx = px^3 - 3x

bx^3 = px^3

b = p

-bx = -3x

b = 3

p = 3

p = 3 , q = -3

Answer 2

We have,

$f(x) = {x}^{4} + p {x}^{3} + 2 {x}^{2} - 3x + q$

And,

$g(x) = {x}^{2} - 1 = (x + 1)(x - 1)$

Then,

$f( - 1) = 1 - p + 2 + 3 + q = 0 \\ = > 6 - p + q= 0$

Also,

$f(1) = 1 + p + 2 - 3 + q = 0 \\ = > p + q= 0$

Adding both the equations, we get;

$q = - 3$

And,

$p = 3$

HOPE THIS COULD HELP!!!