Question

if alpha beta gamma with roots of the equation 2 x cube minus x square + X - 1 is equal to zero then Alpha square plus beta squared plus Gamma square is equals to how much
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Answer 1

Answer:

If α,β,γ are the roots of the equation 2x3-3x2+6x+1=0, then α2+β2+ γ2 is equal to. 255.5 K LIKES. 233.7 K ...

Answer 2

Correct Question: If Alpha Beta Gamma With Roots Of The Equation 2 X Cube Minus X Square + X + 1 Is Equal To Zero Then Alpha Square Plus Beta Squared Plus Gamma Square Is Equal To How Much.

ANSWER:

${ \alpha }^{2} + { \beta }^{2} + { \gamma }^{2} = - \frac{15}{4}$

GIVEN:

Equation - 2x^3 + 3x^2 + 6x + 1 = 0

TO FIND

$\ { \alpha }^{2} + { \beta }^{2} + \ { \gamma }^{2}$

SOLUTION :

We can simply solve the equation as under :

Sum of roots:

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

so,

$\alpha + \beta + \gamma = \frac{3}{2}$

Product of formula :

$\alpha \beta \gamma = \frac{ - d}{a}$

so,

$\alpha \beta \gamma = - \frac{1}{2}$

Sum of products taken two at a time :

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

Now we know that,

α+β+γ)^2=α^2+β^2+γ^2+2(αβ+βγ+γα)

Rearranging,

= α^2+β^2+γ^2=(α+β+γ)^2−2(αβ)

= α^2+β^2+γ^2 =( 3/2 )^2 −2×3

= 9/4 - 6

= - 15/4

hence the answer is -15/4

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