Question

If α and β are the zeroes of the polynomial f(x) = 3x^2 -5x-2, find  α2/  + β2/ ​

Answer 1

Step-by-step explanation:

we know that for a quadratic equation

$a {x}^{2} + bx + c = 0$

Sum of roots

$\alpha + \beta = \frac{ - b}{a}$

For the given equation

$3 {x}^{2} - 5x - 2 = 0$

HENCE

$\alpha + \beta = \frac{5}{3}$

Therefore

$\frac{ \alpha }{2} + \frac{ \beta }{2} = \frac{5}{6}$