Question

find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficient 2 root 3x^2-5x+root3​

Answer 1

quadratic polynomial is given, 2√3x² - 5x + √3 .

2√3x² - 5x + √3 = 0

or, 2√3x² - 2x - 3x + √3 = 0

or, 2√3x² - 2x - √3 × √3 × x + √3 = 0

or, 2x(√3x - 1) - √3(√3x - 1) = 0

or, (2x - √3)(√3x - 1) = 0

or, x = √3/2 and 1/√3

verification : sum of roots = -b/a

LHS = sum of roots = √3/2 + 1/√3 = 5/2√3

RHS = -b/a = -(-5)/2√3 = 5/2√3

LHS = RHS

again, product of roots = c/a

LHS = √3/2 × 1/√3 = 1/2

RHS = √3/2√3 = 1/2

LHS = RHS

hence verified.

Answer 2

$\textbf{Answer is in Attachment !}$