Question

using remainder theorem find the value of k if on dividing 2x^3 + 3 x^2- kx + 5 by X - 2 leaves a remainder 7

Answer 1

Answer:

k = 13

Step-by-step explanation:

Given, f(x) = 2x³ + 3x² - kx + 5.

When f(x) is divided by x - 2, the remainder is 7.

∴ f(2) = 7  

f(2) = 2(2)³ + 3(2)² - k(2) + 5

⇒ 7 = 16 + 12 - 2k + 5

⇒ 7 = 33 - 2k

⇒ -26 = -2k

⇒ k = 13.

Therefore, the value of k is 13.

Hope it helps!

Answer 2

$\bf\huge\textbf{\underline{\underline{Accrording\:to\:the\:Question}}}$  

f(x) = 2x³ + 3x² - kx + 5.

f(x) is divided by x - 2  it leaves 7 as a remainder

f(x) = x - 2

f(x) ⇒ x = 2

$\bf\huge\textbf{\underline{\underline{Put\:Value\:of\:x\:in\:Equation}}}$

f(2) = 7  

f(2) = 2(2)³ + 3(2)² - k(2) + 5

⇒ 7 = 16 + 12 - 2k + 5

⇒ 7 = 33 - 2k

⇒ -26 = -2k

⇒ k = 13.

$\bf\huge{\boxed{\bigstar{\sf\:{Hence\:k\:=\:13}}}}$