Question

find the zeroes of the 4x^2+5√2x-3 and verify the relation between the zeroes and the coefficient of the polynomial

Answer 1

zeroes are √2/4 and -3√2/2 and u can verify the roots by obtaining Sum of Zeroes and Product of Zeroes.

Answer 2

soln: 

Let f(x) = 4x² + 5√2x - 3

let roots of f(x) are α & β

Now, 4x² + 5√2x - 3 = (x - α)(x - β)

or, 4x² + 5√2x - 3 = x² - (α + β)x + αβ

or, x² - (-5√2/4) + (-3/4) = x² - (α + β)x + αβ

equate the like term coefficient in both quadratic equations

or, α + β = -5√2 / 4 & αβ = -3/4, which is required relation.