Question

if alpha and beta are zeros of polynomial 2 X square + 5 x + 1 then find the value alpha + beta + alpha beta

Answer 1

Answer :

p(x) = 2x² + 5x + 1

Sum of Zeroes = (α + β )= (-b/a) = (-5/2)

Product of Zeroes = αβ = c/a = 1/2

Answer to your question :

α + β + αβ = ( α + β ) + αβ

= (-5/2) + 1/2

$\bold{ = \frac{- 5 + 1}{2} }$

$\bold{ =\frac{-4}{2} }$

= -2

Answer 2

Answer:

The value of α + β + αβ is -2.

Step-by-step explanation:

Given if alpha and beta are zeros of polynomial.

$p(x) = 2x^2 + 5x + 1$

Comparing above equation with general form $ax^2+bx+c=0$

⇒ a=2, b=5 and c=1

We have to find the value of α + β + αβ

$\text{Sum of Zeroes = }\alpha +\beta=\frac{-b}{a} = \frac{-5}{2}$

$\text{Product of Zeroes = }\alpha.\beta = \frac{c}{a} = \frac{1}{2}$

α + β + αβ =

          $= \frac{-5}{2}+ \frac{1}{2}$

          $= \frac{- 5 + 1}{2}$

          $=\frac{-4}{2}=-2$

The value of α + β + αβ is -2.