Question

if products of roots of the equation ax²+x+2=0 is 2 , then the sum of roots is​

Answer 1

Answer:

product of roots is c/a=2/a=2

=a=2/2

=a=1

sum of roots is -b/a=-1/a

=-1/1

=-1

Hope this helpful to you

Answer 2

$\large\underline{\sf{Solution-}}$

Let assume that

$\rm :\longmapsto\: \alpha, \beta \: are \: the \: roots \: of \: {ax}^{2} + x + 2 = 0$

Now, it is given that,

$\rm :\longmapsto\: \alpha \beta = 2$

We know,

$\boxed{\red{\sf Product\ of\ the\ roots=\frac{Constant}{coefficient\ of\ x^{2}}}}$

$\rm \implies\: \alpha \beta = \dfrac{2}{a}$

$\rm :\longmapsto\:2 = \dfrac{2}{a}$

$\bf\implies \:a \: = \: 1$

Now, we know that

$\boxed{\red{\sf Sum\ of\ the\ roots=\frac{-coefficient\ of\ x}{coefficient\ of\ x^{2}}}}$

$\rm \implies\: \alpha + \beta = - \: \dfrac{1}{a}$

On substituting the value of a, we get

$\rm \implies\: \alpha + \beta = - \: \dfrac{1}{1}$

$\red{\rm \implies\:\boxed{ \tt{ \: \alpha + \beta \: = \: - \: 1 \: }}}$

More to know :-

$\red{\rm :\longmapsto\: \alpha , \beta , \gamma \: are \: roots \: of \: a {x}^{3} + b {x}^{2} + cx + d = 0, \: then}$

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

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

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