Question

What are the values of p and q, if x - 1 and x + 3 are factors of x3 - px2 - 13x +q?
11​

Answer 1

Answer:

p=22/7 and q=114/7

Step-by-step explanation:

x-1is a factor of p(x) =0

where , p(x)=x^3-px^2 -13x+q

p(x) =0

x-1=0

x=1

p(1)= 1^3 -p×1^2 -13×1 +q

3-2p-13+q=0

-2p+q=10__________(1)

again,

x+3is the factor of p(x) =0

when x= -3

p(-3)=0

(-3)^3-p(-3)^2-13×(-3)+q =0

-27-9p+39+q=0

-9p+q=-12 ________(2)

subtracting equation 1from 2

-2p+q-(-9p+q)=10-(-12)

-2p+q+9p-q=10+12

7p=22

p=22/7

putting the value p in(1)

-2p+q=10

-2×22/7+q=10

-44+7q=70

7q=70+44

7q=114

q=114/7