Find zeroes of the quadratic `sqrt(3)x^(2)-8x+4sqrt(3)` and verify the relation between the zeroes and coefficients.

Answer

N/a

Explanation

Let`" "p(x)=sqrt(3)x^(2)-8x+4sqrt(3)=sqrt(3)x^(2)-6x-2x+4sqrt(3)`
`=sqrt(3)x(x-2sqrt(3))-2(x-2sqrt(3))=(x-2sqrt(3))(sqrt(3)x-2)`
`:. " " p(x)=0`
`implies (x-2sqrt(3))(sqrt(3)x-2)=0`
`implies " " x-2sqrt(3)=0 " " or " " sqrt(3)x-2=0`
`implies " " x=2sqrt(3) " " or " " x=(2)/(sqrt(3))`
`:.` Zeroes of p(x)are`2sqrt(3)` and `(2)/(sqrt(3))`.
Now,`" "` sum of zeroes `=2sqrt(3)+(2)/(sqrt3)=(6+2)/(sqrt(3))=(8)/(sqrt(3))=-((-8))/(sqrt(3))=-("coefficient of" x)/("coefficient of" x^(2))`
and `" "` product of zeroes`=(2sqrt(3))((2)/(sqrt(3)))=4=(4sqrt(3))/(sqrt(3))=("coefficient term")/("coefficient of" x^(2)) " " ` Hence Verified.