Question

IF $\alpha ,\beta ,\gamma$ are the roots of $4x^3-6x^2+7x+3=0$ then find $\alpha \beta +\beta \gamma +\phi \alpha$

Answer 1

Given:- $\alpha ,\beta ,\gamma$ are the roots of equation $4x^3-6x^2+7x+3=0$

To find:- $\alpha \beta +\beta \gamma +\gamma \alpha =?$

As we know that in a cubic equation $a{x}^3+b{x}^2+cx+d=0$, if $p,q,r$ are the roots of equation, then the sum of product of roots is given as-

$pq+qr+rp=\frac{c}{a}$

Now,

$4x^3-6x^2+7x+3=0$

Here,

$a=4,b=-6,c=7,d=3$

Therefore,

$\alpha \beta +\beta \gamma +\gamma \alpha =\frac{c}{a}=\frac{7}{4}$

Hence the correct answer is $\frac{7}{4}$.