Question

If a polynomial x4- 5x3 + x² + kx - 12 is exactly divisible by x² – 5x +4, then find the value of k
​

Answer 1

Answer:

First factories “ x² - 5x + 4 ” to get zeroes.

➡ x² - 5x + 4 = 0

➡ x² - x - 4x + 4 = 0

➡ x(x - 1) - 4(x - 1) = 0

➡ (x - 1)(x - 4) = 0

➡ x - 1 = 0 ; x - 4 = 0

➡ x = 0 + 1 ; x = 0 + 4

➡ x = 1 ; x = 4

Hence, the zeroes are 1 & 4.

Now, substitute the zeroes in given polynomial

➡ (1)⁴ - 5(1)³ + (1)² + k(1) - 12 = 0

➡ 1 - 5(1) + 1 + k - 12 = 0

➡ 1 - 5 + 1 + k - 12 = 0

➡ k - 15 = 0

➡ k = 0 + 15

➡ k = 15

∴ The value of k is ″ 15 ″ .

Step-by-step explanation:

þLÈÄ§È MÄRK MÈ Ä§ ßRÄÌñLÌȧ† ✌✌✌

Answer 2

this is correct explanation