Question

Find the value of k for which the polynomial 2x^3 + 9x^2 - x - k is divisible [2]
by 2x + 3.

Answer 1

Step-by-step explanation:

is it is divisible then reminder should be zero so in picture reminder is 15-k is equal to 0

15-k=0 k =15

Answer 2

Question :-

Find the value of k for which the polynomial 2x³ + 9x² - x - k is divisible by 2x + 3.

Answer :-

The value of k is 15

Solution :-

Let's find the zero of the polynomial (2x + 3),

$\sf\longrightarrow 2x + 3 = 0$

$\sf\longrightarrow 2x = -3$

$\sf\longrightarrow x = \dfrac{-3}{2}$

Now, Putting the value of x in the polynomial,

$\sf\rightarrow 2 {x}^{3}+ 9{x}^{2} - x - k = 0$

$\sf\rightarrow 2 \times {(\dfrac{-3}{2})}^{3} + 9 \times {(\dfrac{-3}{2})}^{2} - \dfrac{-3}{2} - k = 0$

$\sf\rightarrow 2 \times \dfrac{-27}{8} + 9 \times \dfrac{9}{4} - \dfrac{-3}{2} - k = 0$

$\sf\rightarrow \dfrac{-54}{8} + \dfrac{81}{4} + \dfrac{3}{2} - k = 0$

$\sf\rightarrow \dfrac{-54 + 162 + 12 - 8k}{8} = 0$

$\sf\rightarrow -54 + 162 + 12 - 8k = 0$

$\sf\rightarrow -54 + 162 + 12 = 8k$

$\sf\rightarrow 120 = 8k$

$\sf\rightarrow k = \dfrac{120}{8}$

$\sf\therefore k = 15$