Question

if alpha and beta are the zeroes of the quadratic polynomial. 6x2+x-2 then find the value of alpha/ beta +beta/alpha

Answer 1

$6{x}^{2} \: + x - 2$
firstly let us start with finding the zeroes of the equation using factorisation method.

The equation can be rewritten like this after factorisation
$6 {x}^{2} + 4x - 3x - 2 = 0$
$2x(3x + 2) \: - 1(3x + 2) = 0$
$(2x - 1)(3x + 2) = 0$
Now for this we an conclude that the zeroes alpha and beta of the equation are :
$\alpha = 1 \div 2$
$\beta = - 2 \div 3$
so alpha/beta = (1/2)/(-2/3)
= -3/4
and beta/alpha = (-2/3)/(1/2)
= -4/3
Hence the answer is
= -3/4 + (-4/3)
= (-9 - 16)/12
= (-25/12)