Question

verify that -1,1,1/2 are the zeros of the cubic polynomial p(x) = 2x³+x²-2x-1 and then verify the relationship between the zeros and the coefficients​

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

Step-by-step explanation:

p(x) =2x³+x²-2x-1

Let

p(-1) = 2(-1)³+(-1)²-2*(-1)-1

. =-2+1+2-1

=0

Hence , x= -1 is zero of p(x)

Let

p(1) = 2(1)³+(1)²-2*1-1

. = 2+1-2-1

. =0

Hence,x=1 is zero of p(x)

Let

p(-½)=2(-½)³+(-½)²-2*(-½)-1

. = -2/8+1/4+2/2-1

. = -1/4+1/4+1-1

Hence,x=(-½) is zero of p(x)

Relationship between co-efficients

Here,a=2

. ,b=1

. ,c= -2

. ,d= -1

Case (1) : Alpha+Beta+Gamma= -b/a

1+(-1)+(-½)= -b/a

0+(-½)= -½

-1/2= -1/2

:.L•H•S• =R•H•S•

Case(2) : Alpha❌ Beta ➕ Beta❌ Gamma➕ Gamma✖ Alpha=c/a

=1(-1)-1*(-½)-½*1=c/a

= -1+½-½= -2/2

-1 = -1

.'.L•H•S•=R•H•S•

Case (3) :Alpha✖ Beta✖ Gamma

= -d/a

= -1 *1*(-½)= -d/a

1/2= -(-½)

1/2=1/2

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