Question

Obtain the zeros of the quadratic polynomial `sqrt3 x^(2) - 8x+4sqrt3` and verify the relation between its zeros and coefficients.

Answer 1

We have
`f(x) = sqrt3 x^(2) - 8x + 4sqrt3= sqrt3 x^(2) = 6x - 2x+ 4sqrt3`
` = sqrt3 x(x - 2sqrt3) - 2 (x-2sqrt3) = (x - 2sqrt3) (sqrt3x - 2).`
` :. F(x) = 0 rArr (x-2sqrt3)(sqrt3x-2) = 0`
` rArr (x-2sqrt3) = 0 or (sqrt3x-2) = 0`
` rArr x = 2 sqrt3 or x = 2/sqrt2.`
So, the zeros of f(x) are ` 2sqrt3 and 2/sqrt3.`
Sum of zeros = `(2sqrt3+2/sqrt3) = 8/(sqrt(3)) = (-("coefficient of x"))/(("coefficient of " x^(2)),`
product of zeros = `(2 sqrt3 xx 2/sqrt3) = (4sqrt3)/sqrt3 = ("constant term")/("coefficient of " x^(2)).`