Question

If (x + 2) is a factor of x2 + px + 2q and p + q = 4 then what are the values of „p and q?​

Answer 1

Answer:

Factors of x2−3x+2 are (x−1) and (x−2).

Let f(x)=x4−px2+q

Since, f(x) is divisible by (x−1) and (x−2)

∴f(1)=0 and f(2)=0

⇒f(1)=14−p(1)2+q=0

and f(2)=24−p(2)2+q=0

1−p+q=0....(i)

and 16−4p+q=0....(ii)

(i)−(ii), we get

−15+3p=0⇒p=5

putting value of p in eq. (i), we get q=4

Thus, we get

p=5 and q=4.

Step-by-step explanation:

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Answer 2

Answer:

Factors of x2−3x+2 are (x−1) and (x−2).

Let f(x)=x4−px2+q

Since, f(x) is divisible by (x−1) and (x−2)

∴f(1)=0 and f(2)=0

⇒f(1)=14−p(1)2+q=0

and f(2)=24−p(2)2+q=0

1−p+q=0....(i)

and 16−4p+q=0....(ii)

(i)−(ii), we get

−15+3p=0⇒p=5

putting value of p in eq. (i), we get q=4

Thus, we get

p=5 and q=4.