Question

If the divident of an expression x^6+ px^5 + qx^4 - X^2 –X - 3 be x^4 - 1 then the value of p^2 + q^2= ?
(a) 1
(b) 9
(c) 10
(d) 13
if anyone know the solution please describe it ​

Answer 1

Answer:

p² + q² = 10

Step-by-step explanation:

If the divident of an expression x^6+ px^5 + qx^4 - X^2 –X - 3 be x^4 - 1 then the value of p^2 + q^2=

x⁴ - 1  is Divident of x⁶ + px⁵ + qx⁴ - x² - x - 3

=> x⁴ = 1  => x = ±1

x⁶ + px⁵ + qx⁴ - x² - x - 3

at x = 1 wpuld be zero

1+ p + q - 1 - 1 - 3 = 0

=> p + q = 4

at x = -1

1 - p + q - 1 + 1 - 3 = 0

=> -p + q = 2

Adding both

2q = 6

=> q = 3

p = 1

p² + q² = 1² + 3² = 10

p² + q² = 10