Question

Find the zeroes of the polynomials and verify the relation between zeroes of the polynomials 3x^2-8

Answer 1

Heya see the pic below for solution

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Answer 2

Answer:

Given:

• polynomial 3x^2-8

To find :

• The relation between zeroes of the polynomials.

Solving Question:

 We are given the polynomial and are asked to find the the zeros and show the relation .We could do it with the formulas.First have to find the zeros and then substitute the values in it.

If α and β  are the zeros

• α + β =-b/a

• α *β =c/a

Solution:

3x² -8 = 0

⇒ 3x² = 8

or, x² = 8/3

or, x = 2√2/√3 and -2√2/√3

Relationship:

Sum of the roots =

2√2/√3 + (-2√2/√3)

⇒ 0/2√3

⇒ 0 = L.HS

α + β =-b/a

=-b/a = 0/3 = 0  = R.H.S [∵ 3x² +0x -8 is the polynomial ]

Thus, L.H.S = R.H.S

Product of the zeros:

( 2√2/√3)*(-2√2/√3)

⇒ [(2√2)*(-2√2)]/(√3*√3)

or, -8/3

α *β =c/a

=c/a= -8/3

R.H.S = L.H.S