Question

using factor theorem find the value of a if 2x⁴-ax³+4x²-x+2 is divisible by 2x +1

Answer 1

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Answer 2

Given:

if 2x⁴-ax³+4x²-x+2 is divisible by 2x +1

To Find:

using factor theorem find the value of a

Solution:

Factor theorem is used to factor the polynomials or can also be used to find the value of remainder when a polynomial divides a polynomial.

It states that (x-a) is a factor of a polynomial with a degree more than one if f(a)=o and similarly the reverse can also be said if f(a)=0 then (x-a) is a factor of the polynomial.

Now as it is given that 2x⁴-ax³+4x²-x+2 is divisible by 2x +1 then for,

$2x+1=0\\x=\frac{-1}{2}$

For x=-1/2 the polynomial will be equal to zero, Put the values and find the value of 'a', we have

$2*\frac{1}{16}+a*\frac{1}{8}+4*\frac{1}{4} +\frac{1}{2} +2=0\\\frac{a+29}{8} =0\\a=-29$

Hence, the value of a is -29.