Math, asked by anugnya5, 10 months ago

obtain all zeros of polynomial p(x) =2x^4+x^3-14x^2-19x-6 if two of its zeros are -2 and -1​

Answers

Answered by Dvengala
5

Answer:

-1/2 and +3

Step-by-step explanation:

if roots of quadratic equation are -2 and -1 then equation

=x²-(α+β)x+αβ

=x²-(-3)x+2

=x²+3x+2

by division lemma

divisor=dividend x quotient + remainder

i.e. 2x⁴+x³-14x²-19x-6=(x²+3x+2)q(x)+r(x)

x²+3x+2 ) 2x⁴+x³-14x²-19x-6 ( 2x²-5x-3

               2x⁴+6x³+4x²

            ( - )   ( - )   ( - )

                       -5x³-18x²-19x

                       -5x³-15x²-10x

                        ( + )   ( + )   ( + )

                                -3x²-9x-6

                                -3x²-9x-6

                                ( + )   ( + )   ( + )

                                           0

                                ---------------------

q(x)= 2x²-5x-3

     =2x²-6x+x-3

     =2x(x-3)+1(x-3)

     = (2x+1)(x-3)

therefore, roots are -1/2 and +3

Answered by kailashmeena123rm
0

Answer:

polynomial has total of 4 roots

let these are a,b,c,d

now applying properties of these roots

a+b+c+d=-1/2

c+d=5/2. ........1

ab+bc+cd+da=-14/2=-7

-c+cd-2d=-9. .........2

abcd=-3

cd=3÷2=1.5. -c-2d=-9-1.5

c+2d=10.5

on solving 1 and 2 we get c=1.5÷8 and d=8

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