Question

if alpha and beta are the zeroes of polynomial 2y2+7y +5, write the value of alpha + beta + alpha * beta.

Answer 1

Hello,

$\alpha \: \: and \: \: \beta$
Are zeroes of polynomial p(x)
Where
P(x) =2y²+7y+5

Now,
Since the polynomial is quadratic then the relation between the zeroes and the coefficients will be :-

$\alpha + \beta = \frac{ - b}{a} \\ \alpha \beta = \frac{c}{a}$
For any polynomial ax²+bx+c

So,
For p(x)
The sum of the zeroes that is alpha +beta will be - b/a = (-7/2)

Product of the zeroes will be alpha beta =c/a =5/2

Now ,
We have asked the value of
$(\alpha + \beta) + \alpha \beta \\ \frac{ - 7}{2} + \frac{5}{2} \\ \frac{ - 7 + 5}{2} = \frac{ - 2}{2} = - 1$
Hence the answer is negative 1

Hope this will be helping you ✌️