Question

if alpha and beta are the zeros of the polynomial 2 x square - 4 x + 5 then find the value of Alpha minus beta whole square

Answer 1

Answer:

$(\alpha-\beta)^2=-6$

Step-by-step explanation:

Formula used:

$(a-b)^2=(a+b)^2-4ab$

Given:

$\alpha\:and\:\beta$ are zeros of  $2x^2-4x+5$

Then,

Sum of the roots:

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

$\alpha+\beta=\frac{-(-4)}{2}$

$\alpha+\beta=2$

Product of the roots:

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

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

Now,

$(\alpha-\beta)^2=(\alpha+\beta)^2-4\alpha\beta$

$(\alpha-\beta)^2=(2)^2-4(\frac{5}{2})$

$(\alpha-\beta)^2=4-2(5)$

$(\alpha-\beta)^2=-6$

Answer 2

Answer:

(α - β)² = -6

Step-by-step explanation:

if alpha and beta are the zeros of the polynomial 2 x square - 4 x + 5 then find the value of Alpha minus beta whole square

α & β are roots of

2x² - 4x + 5

α + β = -b/a  = -(-4)/2 = 2   ( sum of roots)

αβ = c/a = 5/2   ( Product of roots)

(α - β)²

= (α + β)² - 4αβ

= 2² - 4(5/2)

= 4 - 10

= -6