Question

If alpha and beta are zeros of quadratic polynomial f(x) = 6x2 + x- 2, find the value of αβ + βα

Answer 1

According to given sum,

$if \: \alpha \: and \: \beta \: are \: the \: zeroes \: .$

Then product of zeroes ,

$= > \: \alpha \beta = \frac{c}{a}$

If we compare the quadratic polynomial with
$a {x}^{2} + bx + c$

we get a= 6 ,b=1 , c= -2

$\alpha \beta = \frac{ - 2}{6} = \frac{ - 1}{3}$

From the question,

$\alpha \beta + \beta \alpha = 2 \alpha \beta$
=> 2×(-1/3)

=> -2/3


:-)Hope it helps u.