Question

If (2x-3) is a factor of 2x^4-x^3-3x^2-2x+a, then find the value of 'a'.​

Answer 1

Answer:

-1/2

Step-by-step explanation:

Using factor theorem, when x = 3/2{ from 2( x - (3/2) ) }, numeric value of this expression must be 0.

  For x = 3/2

⇒ 2(3/2)⁴ - (3/2)³ - 3(-3/2)² - 2(3/2) + a = 0

⇒ 2(81/16) - (27/8) - 3(9/4) + 2(3/2) + a = 0

⇒ (81/8) - (27/8) - (27/4) + 3 + a = 0

⇒ (81-27)/8 + (-27+12)/4 + a = 0

⇒ (54/8) - 25/4 + a = 0

⇒ (54 - 50)/8 = - a

⇒ 4/8 = - a

⇒ 1/2 = - a

⇒ -1/2 = a

  Hence the required value of a is - 1/2.