If kx3 + 4x2 + 3x - 4 and x3 - 4x + k leave the same remainder when di

1.	If kx3 + 4x2 + 3x - 4 and x3 - 4x + k leave the same remainder when divided by (x - 3), then the value of k is:
Answer» Correct Answer - Option 2 : -1 Given: Dividend₁ = kx3 + 4x2 + 3x - 4 Dividend₂ = x3 - 4x + k Divisor = (x - 3) Formula Used: Dividend = (divisor × quotient) + Reminder Calculation: x - 3 = 0 Then, x = 3 By substituting the value of x, we'll get kx3 + 4x2 + 3x - 4 = k(3)³ + 4(3)² + 3(3) - 4 = 27k + 36 + 9 - 4 = 27k + 41 ----(i) x3 - 4x + k = 3³ - 4(3) + k = 27 - 12 + k = 15 + k ----(ii) Both the dividends leave equal reminders then equating (i) and (ii) 27k + 41 = 15 + k ⇒ 26k = -26 ⇒ k = -1 ∴ The value of k is -1

If kx3 + 4x2 + 3x - 4 and x3 - 4x + k leave the same remainder when divided by (x - 3), then the value of k is:

Answer» Correct Answer - Option 2 : -1

Given:

Dividend₁ = kx3 + 4x2 + 3x - 4

Dividend₂ = x3 - 4x + k

Divisor = (x - 3)

Formula Used:

Dividend = (divisor × quotient) + Reminder

Calculation:

x - 3 = 0

Then, x = 3

By substituting the value of x, we'll get

kx3 + 4x2 + 3x - 4 = k(3)³ + 4(3)² + 3(3) - 4 = 27k + 36 + 9 - 4 = 27k + 41 ----(i)

x3 - 4x + k = 3³ - 4(3) + k = 27 - 12 + k = 15 + k ----(ii)

Both the dividends leave equal reminders then equating (i) and (ii)

27k + 41 = 15 + k

⇒ 26k = -26

⇒ k = -1

∴ The value of k is -1

Discussion

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