Question

If (x-2) is a factor of x^3-3x^4-ax^3+3ax^2+2ax-4 find the value of a

Answer 1

Solution:-

Given:-

• Polynomial:- (-3x⁴ + x³ -ax³ + 3ax² + 2ax - 4)

=) 3x⁴ - x³ + ax³ - 3ax² - 2ax + 4

• ( x - 2) is the Factor.

To Find:-

• Value of a = ?

Find:-

∵(x - 2) is the Factor of the given Polynomial.

=) x -2 = 0

=) x = 2

P(x) = 3x⁴ - x³ + ax³ - 3ax² - 2ax + 4

=) P(2) = 3(2)⁴ - (2)³ + a(2)³ - 3a(2)² - 2a(2) + 4

=) 0 = 3(16) - 8 + 8a - 3a(4) - 4a + 4

=) 0 = 48 - 4 + 4a - 12a

=) 0 = 44 - 8a

=) 8a = 44

=) a = 44/8

=) a = 5.5

Hence,

a takes the value of 5.5

Answer 2

$\huge{\boxed{\mathbb{ANSWER\::}}}$

Given :-  (x-2) is a factor of x^3-3x^4-ax^3+3ax^2+2ax-4

To find :- The value of "a".

Solution :-

( x - 2 ) = 0

x = 2

Put the value of "x" in the equation :-

x³- 3x⁴- ax³+ 3ax²+ 2ax - 4

p( x )  =  x³- 3x⁴- ax³+3ax²+ 2ax - 4

p ( 2 ) =  (2)³- 3(2)⁴ - a(2)³ + 3a(2)² + 2a(2) - 4

p ( 2 ) =   8 -  3 ( 16 ) - a(8) + 3a(4) + 4a - 4

p ( 2 ) =   8 - 48 - 8a + 12a + 4a - 4

p ( 2 ) =  - 40 + 4a + 4a - 4

p ( 2 ) =   - 44 + 8a = 0

p ( 2 ) =   8a = 44

⇒ a = 44/8

= 11/2

Atlast :-

Hence, the value of "a" = 5.5