Question

For what value of k the polynomial 2x³-kx²+5x+9 is exactly divisible by x+2 ?​

Answer 1

CORRECT QUESTION :-

★ For what value of k the polynomial 2x³ - kx² + 5x + 9 is exactly divisible by x + 2.

GIVEN :-

• the polynomial 2x³ - kx² + 5x + 9 .
• the polynomial 2x³ - kx² + 5x + 9 is exactly divisible by x + 2.

TO FIND :-

• The value of k.

SOLUTION :-

Let,

★ x + 2 = 0

★ x = -2

Therefore,

→ p(x) = 2x³ - kx² + 5x + 9 = 0

→ p(-2) = 2 × (-2)³ - k × (-2)² + 5 × (-2) + 9 = 0

→ 2 × (-8) - k × 4 - 10 + 9 = 0

→ -16 -4k - 10 + 9 = 0

→ -26 -4k + 9 = 0

→ -17 -4k = 0

→ -4k = 0 + 17

→ -4k = 17

→ k = -17/4.

Hence the required value of k is -17/4 for which the polynomial 2x³ - kx² + 5x + 9 is exactly divisible by x + 2.

Answer 2

Given :-

• p(x) = 2x³ - kx² + 5x + 9

To Find :-

• Value of k

Solution :-

Let,

$:\implies\sf x + 2 = 0$

$:\implies\sf x = - 2$

Substituting the value of x in p(x),

$:\implies\sf p(x) = 2x^{3} - kx^{2} + 5x + 9$

$:\implies\sf p(-2) = 2\times(-2)^{3} - k \times (-2)^{2} + 5 \times (-2) + 9 = 0$

$:\implies\sf2\times (-8) - k \times 4 - 10 + 9 = 0$

$:\implies\sf - 16 - 4k - 10 + 9 = 0$

$:\implies\sf - 17 - 4k = 0$

$:\implies\sf - 4k = 17$

$:\implies\sf \underline{\boxed{\blue{\sf k = \frac{17}{- 4}}}}$

Hence, the value of k is 17/- 4.