Question

Q.1.
(a) The remainder obtained by dividing, kx?- 3x + 6 by (x - 2) is twice the remainder
obtained by dividing 3x' +5x -- k by (x + 3). Find the value of k.
[3]​

Answer 1

Q.1.  (a) The remainder obtained by dividing, kx?- 3x + 6 by (x - 2) is twice the remainder  obtained by dividing 3x' +5x -- k by (x + 3). Find the value of k.  [3]

• Given,
• The remainder obtained by dividing, kx?- 3x + 6 by (x - 2)
• x-2 ⇒ x = 2
• = k(2)^2- 3(2) + 6
• = 4k-6+6
• = 4k
• The remainder obtained by dividing, 3x^2+5x-k by (x + 3)
• x +2 ⇒ x = -3
• = 3(-3)^2+5(-3)-k
• = 27 - 15 - k
• = 12 - k
• Now, we have,
• 4k = 2(12 - k)
• 4k = 24 - 2k
• 4k + 2k = 24
• 6k = 24
• ∴ k = 4

Answer 2

The value of k is 4 .

Step-by-step explanation:

Given as :

The quadratic equation

k x² - 3 x + 6

The given quadratic is divided by factor x - 2

As x - 2 is factor , so x = 2 satisfy equation

The remainder = $R_1$ = k ( 2 )² - 3 × 2 + 6 = 4 k - 6 + 6

So ,  $R_1$ = 4 k                   ...............1

Again

The quadratic equation

3 x² + 5 x - k

The given quadratic is divided by factor x + 3

As x + 3 is factor , so x = - 3 satisfy equation

The remainder = $R_2$ = 3 ( - 3 )² + 5 × ( - 3) - k = 27 - 15 - k

So ,  $R_2$ = 12 - k                      ...........2

According to question

remainder obtain by dividing the first equation = twice remainder obtain by second

From e1 and eq 2

i.e  $R_1$  = 2 $R_2$

Or, 4 k = 2 ( 12 - k)

Or, 4 k = 24 - 2 k

Or, 4 k + 2 k = 24

or, 6 k = 24

∴     k = $\dfrac{24}{6}$

i.e k = 4

So, The value of k = 4

Hence, The value of k is 4 . Answer