Question

if alpha and beta are zeros of f (x) = 6 X square + X - 2 find Alpha / beta + beta / Alpha

Answer 1

Hiii friend,

P(X) = 6X²+X-2

Here,

A = 6 , B = 1 and C = -2.

Alpha + Beta = -B/A

Alpha + Beta = -1/6

And,

Alpha × Beta = C/A

Alpha × Beta = -2/6 = -1/3

Therefore,

Alpha/Beta + Beta/Alpha

=> (Alpha)² + (Beta)²/Alpha × Beta


=> (Alpha+Beta)² - 2 × Alpha × Beta/Alpha × Beta

=> (Alpha+Beta)² - 2

=> (-1/6)² - 2

=> 1/36 -2

=> 1 - 72/36

=> -71/36



HOPE IT WILL HELP YOU...... :-)

Answer 2

Hey.. I think this can be ur answer!!

Alpha and beta are zeroes of 6x2 +x - 2

Alpha + beta = - b/a = - 1/6
Alpha * beta = c/a = - 2/6 = - 1/3

Now,
Alpha /beta + beta /alpha
=alpha 2 + beta 2/alpha *beta
= (alpha + beta) 2 - 2alpha *beta /alpha *beta
=(-1/6)2 - 2(-1/3) * (-3)
=1/36 - 2