Question

If (x + a) is a factor of x^3 + ax^2 – 3x + a + 5, then the value of a is
a. 4/5.
b. -5/4.
c. -4/5.
d. 5/4.​

Answer 1

Answer:

$\large\boxed{\bigstar \: \: (b) \: a = - \frac{5}{4} \: \: \bigstar }$

Step-by-step explanation:

→ Given:-

(x+a) is a factor of x³+ax²-3x+a+5.

→ To Find:-

The Value of a.

→ Solution:-

g(x)=x+a=0

x=(-a)

p(x)=x³+ax²-3x+a+5

Now, putting x=(-a):

p(-a)=(-a)³+[a×(-a)²]-3(-a)+a+5=0

-a³+a³+4a+5=0

4a=(-5)

$a = \frac{ (- 5)}{ 4}$

$\boxed{a = - \frac{5}{4} }$

Answer 2

Step-by-step explanation:

Answer:

\large\boxed{\bigstar \: \: (b) \: a = - \frac{5}{4} \: \: \bigstar }

★(b)a=−

4

5

★

Step-by-step explanation:

→ Given:-

(x+a) is a factor of x³+ax²-3x+a+5.

→ To Find:-

The Value of a.

→ Solution:-

g(x)=x+a=0

x=(-a)

p(x)=x³+ax²-3x+a+5

Now, putting x=(-a):

p(-a)=(-a)³+[a×(-a)²]-3(-a)+a+5=0

-a³+a³+4a+5=0

4a=(-5)

a = \frac{ (- 5)}{ 4}a=

4

(−5)

\boxed{a = - \frac{5}{4} }

a=−

4

5