Question

obtain the zeros of the quadratic polynomial root3x^2-8x+4root3 and verify the relation between its coefficients?

Answer 1

hi friend,


√3x²-8x+4√3=0

√3x²-6x-2x+4√3=0

√3x(x-2√3)-2(x-2√3)=0

(√3x-2)(x-2√3)=0

x=2/√3,2√3


we know sum of roots ,= - x coefficient /x² coefficient

2/√3+2√3=8/√3


8/√3=8/√3


hence verified


we know that product of roots is constant term /x² coefficient

(2/√3)(2√3)=4√3/√3

4=4


hence verified




I hope this will help u ;)

Answer 2

Given polynomial,
√3x²-8x+4√3=0
√3x²-6x-2x+4√3=0
√3x(x-2√3)-2(x-2√3)=0
(x-2√3)(√3x-2)=0
x-2√3=0
x=2√3

√3x-2=0
√3x=2
x=2/√3

The zeroes of the polynomial are 2√3 and 2/√3.

Relation between the zeroes and coefficients:-

Sum of zeroes=2√3+2/√3=[(2√3)√3+2]/√3
=2(3)+2/√3
=8/√3= -x coefficient /x² coefficient

Product of zeroes=(2√3)(2/√3)
=4√3/√3=constant/x² coefficient

hope it helps