Question

if Alpha and beta are zeroes of the polynomial f(x)=6x^2+x-2,find the value of (alpha/beta+beta/alpha)​

Answer 1

Answer: $=-\frac{25}{12}$

Step-by-step explanation:

To find roots, f(x) =0

$0 = 6x^2 +x-2\\0= 6x^2+4x-3x-2\\0= 2x(3x+2)-1(3x+2)\\0 =(2x-1)(3x+2)$

Hence $2x-1=0$ or $3x+2 = 0$

$\alpha =1/2\\and \\ \beta =-2/3$

Now  

$\frac{\alpha }{\beta } +\frac{\beta }{\alpha }$

$=\frac{1/2}{-2/3} + \frac{-2/3}{1/2} \\\\= -\frac{3}{4} + (\frac{-4}{3} )\\\\=-\frac{25}{12}$

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