Question

root 3 x square - 8 x + 4 root 3 find the zeros of the quadratic polynomial and verify the relationship between the zeros and the coefficient​

Answer 1

Answer:

$\sqrt{3}$x^2-8x+4$\sqrt{3}$

where α+β=8/√3

and αβ=4

now we reform this into another quadratic equation

x^2-(α+β)x+αβ=x^2-(8/√3)x+4=x^2-8/√3x+4

=x^2+x(-2/√3-6/√3)+4                       where 8/√3 is sum and 4 is product

=x(x-2/√3)-6/√3(x-2/√3)

=(x-6/√3)(x-2/√3)                            x-6/√3=x=6/√3     x-2/√3=x=2/√3

sum of zeroes =α+β=6/√3+2/√3=8/√3

product of zeroes=αβ=6/√3*2/√3=4

hence the relationship is verified