Question

Find the value of k, if (2x - 3) is a factor of x3 + 2x2 - 10x + k.​

Answer 1

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Answer 2

Answer:

57/8

Step-by-step explanation:

  Using factor theorem, as ( 2x - 3 ) is a factor of this, when x = 3/2, value of this expression will be 0.

⇒ (3/2)³ + 2(3/2)² - 10(3/2) + k = 0

⇒ (27/8) + 2(9/4) - 5(3) + k = 0

⇒ (27/8) + (9/2) - 15 + k = 0

⇒ ( 27 + 36 - 120 )/ 8 = - k

⇒ - 57/8 = - k

⇒ 57/8 = k

Hence the required value of k is 57/8