Question

check by division algorithm whether the polynomial 2x²+3x+4 is a factor of the polynomial 2x⁴+7x³+10x²+14x+8​

Answer 1

Step-by-step explanation:

Method of finding the remaining zeros of

a polynomial when sum of its zeros are

given:

We firstly write the factor of polynomial

using given zeros and multiply them to

get g(x). Then divide a given polynomial

by g(x).

The quotient so obtained give other zeros of given polynomial and we factorise it to get other zeros.

SOLUTION:

Let f(x) = 2x4 - 2x³ −7x² + 3x + 6

Given :

(x+√3/2) & (x-√3/2) are the two factors of given Polynomial f(x).

(x+√3/2) (x-√3/2) = x²- 3/2 = (2x²-3)/2

= (2x²-3)/2=0

2x²-3 is a factor of given Polynomial f(x) Divide f(x)=2x² − 2x³ −7x² + 3x + 6 by 2x²-3

[DIVISION IS IN THE ATTACHMENT.]

f(x)=2x² − 2x³ −7x² + 3x +6 = (2x²-3)(x²-x-2)

= (2x²-3) (x-2)(x-1)

f(x)=0

= (2x²-3) =0, (x-2)= 0, (x-1)=0 x= √3/2, -√3/2, 2