Question

find the value of k if polynomial x is equal to K multiply x cube minus 13 x square -( k - 7 )x x + 7 is divisible by 3 X + 2​

Answer 1

Solution:

It is given that if polynomial f(x)= kx³ -13x² -(k -7)x + 7 is divisible by 3x + 2.

Find root of Equation:

f(x)= 3x + 2

⇒ 3x + 2 = 0

⇒ 3x = -2

⇒x = -2/3

Substitute value of x in Equation:

f(x)= kx³ -13x² -(k -7)x + 7

⇒ kx³ -13x² -(k -7)x + 7 = 0

⇒ k(-2/3)³ - 13(-2/3)² - k(-2/3) + 7(-2/3) + 7 = 0

⇒ k(-8/27) -13(4/9) + 2/3k - 14/3 = 0

⇒(-8/27)k -52/9 + (2/3)k - 14/3 = 0

⇒ (-26/27) - 94/9 = 0

⇒ (-26/27)k= 94/9

⇒ -26k = 94/9 × 27

⇒ -26k = 282

⇒ k = 282/-26

⇒ k = -141/13

Therefore, Required Value of k is -141/13.