Question 20
If x + 2a is a factor of x5–4a2x3+2x+2a+3, then find the value of a.
Open in App
Solution
Let p(x)=x5–4a2x3+2x+2a+3
Since x + 2a is a factor of p(x), p (-2a) = 0 [Using Remainder Theorem]. ∴(−2a)5–4a2(−2a)3+2(−2a)+2a+3=0 ⇒−32a5+32a5–4a+2a+3=0 ⇒−2a+3=0 ⇒2a–3=0 ∴a=32
Hence, the value of a is 32.