Question

find the value of c so that the polynomial 2x^3-7x^2-x+c is exactly divided by x+3/2

Answer 1

ANSWER:

Given:

• p(x) = 2x³ - 7x² - x + c

To Find:

• Value of c so that p(x) is exactly divisible by (x + 3/2)

Solution:

We are given that,

⇒ p(x) = 2x³ - 7x² - x + c

We need to find the value of c, for which p(x) is perfectly divisible by (x + 3/2).

So, that means p(3/2) is 0.

⇒ p(x) = 2x³ - 7x² - x + c

⇒ p(3/2) = 2(3/2)³ - 7(3/2)² - (3/2) + c

⇒ 0 = 2(27/8) - 7(9/4) - 3/2 + c

Simplifying the terms,

⇒ 27/4 - 63/4 - 3/2 + c = 0

Taking LCM,

⇒ (27 - 63 - 6 + 4c)/4 = 0

Transposing 4 to RHS,

⇒ 27 - 63 - 6 + 4c = 0

⇒ -42 + 4c = 0

Transposing 42 to RHS,

⇒ 4c = 42

Transposing 4 to RHS,

⇒ c = 42/4

Simplifying the terms,

⇒ c = 21/2

Therefore, the value of c for which p(x) is completely divisible by (x + 3/2) is 21/2.