Question

For what value of k the polynomial 2x^3-kx^2+5x+6 is exactly divisible by x+2

Answer 1

Answer:

K = - 1

Step-by-step explanation:

$polynomial = 2x {}^{3} - k {x}^{2} + 5x + 6$

SINCE IT IS EXACTLY DIVISIBLE BY (x +2)

SO,

POLYNOMIAL = 0 IF ( x = - 2 ).

NOW ,

$2( - 1) ^{3} - k( - 1)^{2} + 5( - 1) + 6 = 0$

ON FURTHER SOLVING WE WILL GET :

- 2 - K - 5 +6 = 0 .

K = - 1

HOPE THIS HELPS YOU

Answer 2

GIVEN :-

• P(x) = 2x³ - kx² + 5x + 6

TO FIND :-

• The value of k.

SOLUTION :-

➵ Let x + 2 = 0

➵ x = -2

Now put he value of x in P(x).

⇒ P(x) = 0

⇒ 2x³ - kx² + 5x + 6 = 0

⇒ 2 × (-2)³ - k × (-2)² + 5 ×(-2) + 6 = 0

⇒ 2 × (-8) - k × 4 - 10 + 6 = 0

⇒ -16 - 4k - 10 + 6 = 0

⇒ - 26 + 6 - 4k = 0

⇒ - 20 - 4k = 0

⇒ - 4k = 0 + 20

⇒ - 4k = 20

⇒ k = -20/4

⇒ k = -5

Hence the value of k is - 5

VERIFICATION :-

➵ Here we found k = (-5)

∴ Replace k as (-5) in P(x).

⇒ P(x) = 2x³ - kx² + 5x + 6

⇒ P(x) = 2x³ + 5x² + 5x + 6

Now put the value of x,

⇒ P(x) = 2x³ + 5x² + 5x + 6

⇒ P(-2) = 2 × (-5)³ + 5 ×(-2)² + 5 ×(-2) + 6

⇒ -16 + 20 - 10 + 6

⇒ 26 - 16 + 10

⇒ 26 - 26

⇒ 0

Hence we found the Remainder 0

Hence VERIFIED