Question

if alpha, beta and gama are the roots of 4x^3-6x^2+7x+3=0 then find the value of alpha.beta + beta.gama + gama.alpha

Answer 1

Answer:

201kbhbjeehehu3h3heh

Answer 2

$\green{ \boxed{ \bigstar \: \: \: \: \bf \alpha \beta + \beta \gamma + \gamma \alpha = \frac{7}{4}}}$

Step-by-step explanation:

We know that,

If

$\pink{\rm \bigstar\: \alpha , \beta , \gamma \: are \: zeroes \: of \: a {x}^{3} + b {x}^{2} + cx + d, \: then}$

$\boxed{ \bf{ \: \alpha + \beta + \gamma = - \dfrac{b}{a}}}$

$\boxed{ \bf{ \: \alpha \beta + \beta \gamma + \gamma \alpha = \dfrac{c}{a}}}$

$\boxed{ \bf{ \: \alpha \beta \gamma = - \dfrac{d}{a}}}$

Now given the polynomial :

$\bf \: 4 {x}^{3} - 6 {x}^{2} + 7x + 3 = 0 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf \: \alpha , \: \beta \: and \: \: \gamma \: are \: the \: zeroes \: of \: that \: polynmial \\ \\ c\:=\:7\:\:\:\:\:\:and\:\:\:\:a\:=\:4\\\\ \bf \green{ \bf \: \therefore \: \alpha \beta + \beta \gamma + \gamma \alpha = \frac{7}{4} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$