Question

Obtain all zeroes of the polynomials f(x)=2x^{4}+x^{3}-14x^{2}-19x-6 if two zeroes are -2 and -1

Answer 1

Answer:

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Answer 2

ANSWER:

alpha=-2 and beta=-1

p(x)=x^2-[alpha + beta]x+[(alpha)(beta)]

=x^2-[(-2)+(-1)]x+[(-2)(-1)]

=x^2-(-3x)+(2)

=x^2+3x+2

=x^2+3x+2

☆Divide the polynomial

f(x)=2x^4+x^3-14x^2-19x-6

by p(x)=x^2+3x+2 (division is attached)

We get the QUOTIENT

2x^2-5x-3

Factorise the quotient:

2x^2-5x-3

=2x^2-5x-3

Coefficient of x^2 × constant

=(2)×(-3)=-6

Coefficient of x =-5

-6

/\

/ \

/ -5 \

/ \

/ \

-6 = -3 +1

2 1 2

=(x-3)(2x+1)

x-3=0 2x+1=0

x=3 x=-1/2

The other zeroes are 3 and -1/2.

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