Question

If on dividing 2x³ + 6x² – (2k – 7)x + 5 by x + 3, the remainder is k – 1 then the value of k is

विकल्प

• 2

• – 2

•  – 3

• 3

Answer 1

f(x) = 2x³ + 6x² – (2k – 7)x + 5
g(x) = x + 3
Remainder = k – 1
If x + 3 = 0,
then x = –3
∴ Remainder will be
f(–3) = 2(–3)² + 6(–3)² – (2k – 7)(–3) + 5
= –54 + 54 + 3(2k – 7) + 5
= –54 + 54 + 6k – 21 + 5
= 6k – 16
∴ 6k – 16 = k – 1
6k – k = –1 + 16
⇒ 5k – 15
k = `(15)/(5)` = 3
∴ k = 3.