Answer:
p = - 5, q = 10
Step-by-step explanation:
If f(x) is divisible by (x - h) then f(h) = 0
Here
f(x) = [tex]x^{4}[/tex] + x³ - 7x² + px + q
dividing by (x - 1) with h = 1 , then
[tex]1^{4}[/tex] + 1³ - 7(1)² + p + q = 0, that is
1 + 1 - 7 + p + q = 0
- 5 + p + q = 0 ( add 5 to both sides )
p + q = 5 → (1)
Dividing by (x + 2) with h = - 2 , then
[tex](-2)^{4}[/tex] + (- 2)³ - 7(- 2)² - 2p + q = 0 , that is
16 - 8 --- 28 - 2p + q = 0
- 20 - 2p + q = 0 ( add 20 to both sides )
- 2p + q = 20 → (2)
Subtract (1) from (2) term by term, thus eliminating q
- 3p = 15 ( divide both sides by - 3 )
p = - 5
Substitute p = - 5 into (1) and solve for q
- 5 + q = 5 ( add 5 to both sides )
q = 10
